Considering its possible they'd meet because of family reunions, how would you think a Maosuba and Rykeares meeting would go?
What a fun question! So much fun, in fact, that I got a little carried away with the doodling and may have ended up spending an ungodly amount of time on that (slow artist syndrome). So, thank you for this question, and moreso, thank you for your patience!
(Usual disclaimer, this is pretty much all headcanon based on my personal playthroughs of RF5 and GoA, definitely not meant to be read as a general analysis of any kind especially in regards to the protags. Post also contains spoilers for both games, so proceed with caution!)
For starters, I do believe Mauro already met Ares + Ryker prior to Azuma during his stopover in Rigbarth (and traveler that he is, I doubt he wouldn't have stayed at least a few days to enjoy what Rigbarth has to offer). By this point, Ares and Ryker have been married w/ kids within the range of five years - a decade (gauging based off Hina) and are pretty settled. But the two of them were a lot more reckless when they were younger, dungeon-diving late into the night in search of treasure on a fairly regular basis. I think Mauro's passion for treasure would remind Ares of those glory days quite a bit, and he'd find that pretty nostalgic + charming.
(Long post warning: continued under the cut.)
As for Ryker...I think it's a bit more of a toss up since Mauro is characteristically very similar to Palmo (eccentric, exuberant, loud, sentimental/emotional, kindhearted, passionate, friendly...list goes on)...and we know that Ryker absolutely adores and respects Palmo. But also, Palmo is Palmo. He's both a father and mentor to Ryker. Mauro is a weird little cousin that drops out of the sky one day who might be a tad bit too nosy for Ryker's tastes. (Also LOUD.)
I imagine Mauro sleeps in the airship as per usual during his stay in Rigbarth (considering in Azuma he opts for that rather than book a room at the inn, he must find it comfortable, or at least comforting). This is a good thing because even though Ryker's old room could technically be a guest room I don't think he'd want Mauro anywhere near the place. Ryker's a very private person and has a lot of things hidden away here and there - notes under the desk, drawers with false bottoms...exactly the sort of thing that'd make Mauro's treasure radar go absolutely wild. It's not snooping, of course. It's simply his treasure hunter's instinct!
With all that said I'm not sure they'd get to know each other entirely too well during that initial meeting (Mauro would certainly try, what with his friendliness, but considering his time in Rigbarth is limited and he's plenty excited for Azuma, he's also got a lot else to occupy his mind and time). I do imagine that Ryker confronted Mauro to make him swear to keep Hina safe though. We all know how much he looks out for those kids (which I think would hold even now that they're kids no longer).
(On a side note, I hc that Mauro's "marvelous swimsuit" was gifted to him by Palmo before he left for Azuma - it features his bird motif + colors and I feel that presenting the tiniest pair of shorts as a send-off gift just seems like a very...Palmo thing to do.)
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Imagining Ryker and Mauro interacting is fun because in many ways, they're polar opposites - Ryker is more reserved with his true feelings, Mauro wears his heart on his sleeve. Ryker is chill + sleepy while Mauro's got up-to-eleven energy. Ryker is easily flustered, while Mauro is so earnest he's usually the one doing the flustering. Low-key vs. over-the-top. Something-to-hide vs. nothing-to-hide. Cool vs. warm. In many ways, they're much like the moon and sun.
But for all their differences, they also have quite a bit in common - a love for treasure, the passion to hold and chase a dream (and, apparently, the capacity to fall in love so completely so as to be willing to let go of that dream), a flair for the dramatic, a healthy dose of self-confidence, a curious nature (I'd say they're actually both pretty nosy, it comes with the curiosity! ...just that Ryker has an aversion to being looked into himself, whereas Mauro's generally an open book).
They both consider the MC to be the greatest treasure there is / a treasure like no other should you choose to pursue them. (Deja vu for real. Turns out my lot in life is to be a de Sainte-Coquille family treasure...orz)
...Which is funny, because it makes their stories kind of hilariously parallel - imagine Mauro showing up in Rigbarth gushing about his dream to find a treasure like no other, and Ryker thinking...heh, too bad, the world's greatest treasure is already mine...only for Mauro to show up again at some point to say, look, I found my treasure! ...and it's literally also an Earthmate. Considering how rare/special Earthmates are, what even are the chances?
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I do think Mauro + Subaru would visit Rigbarth on their tour of Adonea (Mauro does have family there and with it being Hina's hometown, I think Subaru would love to see it). So I think they'd end up meeting Ryker + Ares at some point even if not for the DSC reunions. But I do think them meeting at one of these gatherings is a fun idea and possibly a good way for them to get acquainted!
I don't imagine Ryker is the type to usually attend such reunions (prior to his character event I think he'd kind of just...disappear should one occur. His feelings on family are complicated at this point and I think there'd be a part of him that hasn't quite accepted that he's part of the DSC family). But after coming to terms with his past and settling with a family of his own, I think he'd be more open to the idea of getting to know the extended family (even if more for Palmo's sake, and perhaps with some gentle coaxing from Ares).
That said, I think being surrounded by the entire DSC clan all at once would be a bit too much for someone like Ryker (and with the conversation inevitably veering toward food-related topics I doubt it would hold his interest either), so I think he'd likely sneak off somewhere in the middle of things to catch some peace and quiet with Ares.
...which I think would set off a certain someone's treasure hunter's instinct.
Not that Mauro's eavesdropping treasure hunter's instinct would actually work here - another thing I find fun about potential interactions between these two is there's a lot of fun to be had with Mauro's treasure hunter's instinct vs. Ryker's incredibly sharp senses/alertness. Ryker's secretiveness sparks Mauro's curiosity, but Ryker catches him every time. In this case though, getting called out into the open is the icebreaker that gets everyone talking, which I think is a treasure in itself as far as Mauro's concerned.
As for the two protagonists, since they're both fairly laid-back and friendly they'd get along pretty well. If they had the opportunity to talk at length they'd find they have a lot in common, perhaps a bit too much in common! They're both altruists who have put themselves through the wringer for the sake of the world and others. Not to say they're exactly the same. Their respective journeys have shaped them in different ways, so in that sense they'd also have a lot to learn from each other.
Ryker/Ares and Mauro/Subaru are two very different couples though. Ares isn't as shy as Ryker when it comes to romantic matters but they're still a relatively private couple (much more affectionate away from prying eyes, and not so much for pda). Whereas after being with Mauro for awhile Subaru got used to his open style of affection and is much less embarrassed by it than he was when they first started out. For Subaru, holding hands with or embracing Mauro out in public is no big deal. And for someone like Ryker, having to watch any of this is downright embarrassing.
(Ares is mostly joking here, he just can't help but tease Ryker from time to time.)
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Considering their shared history of treasure hunting, I think it'd be fun if both couples went on an expedition together - they'd definitely all be down for it. Ryker and Mauro both take their treasure hunting seriously, plus Ryker is pretty competitive so they could even make a game of it. And with two Earthmates on board, what could possibly go wrong?
Enter yet another fun contrast: Ryker's expert trap detection / disarming skills versus Mauro's "bad luck" (aka what does this thing do?).
Ryker is used to dealing with traps. Placing them, detecting them, avoiding them, disarming them...it's all second nature for a (former) phantom thief. And he's used to having to put those skills to the test to look out for those who...aren't so aware (read: Ares). More than once he's had to stop Ares from walking right into a well-concealed trap or yanking him out of harm's way, but while he wishes Ares would be just a little less dense in regard to such dangers, it's also well within his expert capability to handle.
What he's not used to nor prepared for is the utter force of chaos that is Mauro Panforte de Sainte-Coquille.
If Mauro's genuine bad luck triggers half the traps in a dungeon, his curiosity inevitably triggers the other half. Walking blindly into rooms that scream danger. Touching every little thing, even if it's obviously suspicious. Especially if it's obviously suspicious. Triggering traps ON PURPOSE.
Ever seen that scene in Dungeon Meshi where Chilchuck goes to disarm the trap room and tells everyone how to avoid the traps, and then Senshi just walks through it and triggers literally everything? ...I imagine it's something like that. Ryker has absolutely no idea how Mauro can plausibly still be alive.
Ryker's usually pretty chill. It takes a lot to truly rile him up so long as your name isn't Martin. But I think this could possibly do it. After all, it's a level of carelessness that puts everyone in danger.
(Ares is perhaps more forgiving because he's not the trap expert Ryker is and knows he's made similar mistakes, and he always feels bad when he goofs up like that. ...Subaru still gets his condolences though.)
The silver lining is that with the way Mauro's luck usually works, despite everything everyone makes it out relatively unscathed. At the very least, much less-scathed than they ought to be. And although Mauro typically isn't so lucky in this regard, with the others' luck combined I think they'd make away with at least a little treasure!
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Bonus section: this is much more theoretical since as it stands there isn't much reason for Mauro to hang around Rigbarth for too long...but if they spent enough time together, I kind of imagine Ryker and Mauro could plausibly form an almost sibling-like relationship. Mauro would absolutely exasperate Ryker with his too-bright, too-loud, too-cheery too early in the gods damned morning, and Ryker would absolutely prank and tease Mauro to get back at him. They're both big kids at heart, really.
On the other hand, Mauro would have nothing but genuine praise and enthusiasm for Ryker's blueprints + projects, which I think would mean a lot to Ryker (even if he wouldn't admit it). He's used to people seeing him as nothing but lazy and he does tend to doubt himself and his abilities, unsure if he can live up to Palmo's standards. And Ryker would worry about Mauro in turn and show up to haul him out of whatever predicament his curiosity lands him in. Maybe try to actually teach him a thing or two about detecting/disarming traps, if any of it actually sticks. To Ryker, Mauro may as well be another one of the kids he's got to keep an eye on (he's probably fairly close in age to Julian + Hina at this point anyway).
Not exactly your question, but it's a fun dynamic to think about!