My humble answer is...
I LOVE IT.
(Romance-y stuff first then the section below that is…other activities)
Content Warning for any other readers: Canon x Canon, Crossdressing, BDSM Dynamics, tons and tons of personal interpretations and almost a fic outline
MY FRIEND, WHAT HAVE YOU DONE??
At first glance someone might think, "They're too unalike, they have no common interests. Barbatos is too cool for him and Levi hates him because he's successful, confident and widely respected." And one would be wrong!! The main things they have in common are Gaming, Sewing, Creating Artwork and Cooking (in that order only because Levi's still a hobbyist and Barbatos's love of baking and cooking is on par with Levi's fanatical love of Ruri-chan.)
Barbatos may not be into watching anime or reading manga, but he buys merch for Diavolo and is supportive of a substantial number of things Diavolo does (which extends to Levi hehehe) but he is a major gamer. In two different events (Cyber and Smash Devils) and in a variety of OM daily chats he games with Levi as well as plays his recommended games (and Levia-chan gets his little scaly ass handed to him when they play!)
One of my favorite scenarios for them developing into a couple is that Levi finds out what an awesome sewist he is (HDD 2021 card "An Amazing Outfit for You" and Belphie's Plushie card are two examples) and is awestruck. "PLEASE teach me your techniques! What is your secret?!?" But Barbatos doesn't just teach him, he makes him things too! Costumes, does his Makeup, Props, plushies and food replication!
I headcanon that Barbatos takes Diavolo and Leviathan to conventions too, they could absolutely group cosplay. Barbatos is a gamer so we know they already chat and hang out online, and Barbatos has been to his room multiple times now so it's not implausible that they'd like to hang out 1 on 1 too. (In Otaku Podcast Mini Barbatos scares the shit out of him by how familiar he mades himself with Levi's room and the secret box he has) If LEVI lets someone not just touch his things and explore them (oop lol that sounds….) but lets him rearrange his things and even advise him on what to do about them you know that is some deep, deep, trust and approval. He admires him a lot too, he experiences jealousy and idolizes him too so we know that Levi already has strong feelings about him!!
I think that whenever Barbatos would show him approval or acknowledgement it would direct hit something deep inside him that is painfully wounded and mend a little crack in his heart. I think Levi needs to impress others, but won't admit it. He's too caught up in the "normies can kick rocks! Get rekt! I don't care what those people think!" but he obviously felt the pressure of Barbatos's expectations to a degree near that of Lucifer's because he was almost in tears from the stress of working with them (he chose them!) during Luke's Birthday in 2022. So I think making him proud of him or surpassing his expectations (Shrodinger's High/Low expectations lol) would be important to him. I don't really read Levi's (or anyone else's) romantic options and don't go out of my way to read his cards, so this is mostly based off of my interpretations from events and storylines. I don't feel confident in my characterization either. Somebody is going to hate on me for that some day. I can feel it.
Oh, but back to the topic. So they start hanging out in order to do sewing and that leads to talking about all kinds of things and warming up more. Levi is like, "Wait what?? You mean…he's not as intimidating and far above us as I thought???" Barbatos cooks for him whenever he gets hungry or has already prepared bentos and other anime themed foods and teaches him how to recreate/copycat for him too. So as they bond Levi accepts that he really is a friend of his and not just his big brother's coworker/the Royal Butler/Popular Guy and humoring him. He subtly starts to tell him about his interest in crossplaying too (Legendary Dame, HELLO~) and while that's not really something Levi HIDES (he did) that Barbatos responds positively and supportively (Diavolo too, he cosplayed RURI and Barbatos cosplayed Azuki-tan in support and to show their appreciation for Levi and his interests in the S2 Anime!)
So Levi dresses up and is all blushy and nervous and feeling excited and happy because he's just so COOL about this!? AND GIVES MAKEUP ADVICE THAT EVEN ASMO HADN'T KNOW??? (Dame card) And the first thing Barbatos does is tells him he looks cute and wears it well, he compliments his dress and makeup! (Or beautiful, depends on whether he's in a magical girl outfit or if he's cosplaying someone elegant like the Kuudere Elf Queen Seraphina)
So after this, one thing leads to another and Barbatos crossplays with him (He self vowed that Legendary Dame was never again, but I am going to just say that that doesn't mean he's banned from other elegant femme attire) Levi doki-dokis like crazy! So now he's down bad for Lady!Barbatos, "B-but that's just because of the character he's portraying, right?? I don't have a crush on my big brother's co-worker/the Royal Butler/The Popular Guy????"
Barbatos got so excited about sewing for MC and dressing MC up that not once, but twice he gets carried away and starts taking measurements or holding clothes up to their figure (promptly apologizes and then we can't even acknowledge it) So maybe that happens with Levi too and now that Levi has doki-dokis when Barbatos gets that close to him HORMONAL EXPLOSION~. "Ooooookay, that definitely isn't just because of the character he was cosplaying" lols anxiously
Where this goes is going to be non-specific because I love endless possibilities, but definitely gets intimate. Possibly the first time they get frisky is while in cosplay (Levi is like a teenage boy in a 30 year old body, I swear. And then you have Barbatos who pops off with those romantic and suggestive dialogues to tease like WHAAAAAAAT??? So, he would totally egg (lol unintended) him on and turn him into a flustered sweaty mess without even taking his own clothes off.) 70% probability of while couple cosplaying a yuri or yaoi ship, but they go all the way as themselves and after a barrier is overcome (Levi's self-esteem and his doubts about whether the person he's into is ACTUALLY? FOR REAL??? SERIOUS??? You're not just messing with me and going to humiliate me and then gloat about it because I'm a socially awkward otaku loser and you're a hot demon butler whose effortlessly perfect?) So it would be a combination of shame/comfort and hurt/comfort…maybe?
Their first anniversary gift from Barbatos would be a fully custom designed outfit for them to wear, there would be a necklace or other jewelry included in a hidden treasure way and it would have an engraved message on the back/inside along with a handwritten letter. Levi's would be a physical photo album with their cosplay adventures and outings/pilgrimages/foodie tours and one-day vacation photos with sweet notes and memories written on the backs of them. (I'm not very good at this type of romance tbh, but memories and keepsakes are important to them both)
On a side note they have SO MUCH KINK CHEMISTRY. Levi wants to be bullied, humiliated, called names and degraded? Barbatos is absolutely brutal with all of this, and probably has Dacryphilia to some extent (cough MAMMON) He would not be against-- on second thought this part got too explicit. [SNIP]
He would be creative at this in subtle ways, even during normal group conversations, that would leave Levi speechless and doki-doki'ing. On the flipside, Barbatos praises and shows his gratitude in significant ways so this would extend to intimate activities and he is a very attentive lover/dom who anticipates the needs of others so he would give Levi aftercare and approval tailored to each scene, "feed and water" him (Barbatos…why did you word it like that before?) and then tuck him into bed with a goodnight kiss. (Barbatos doesn't stay overnight of course. He has a Diavolo at home to think of after all and Diavolo is prone to mischief and misbehavior when he is away.) He would also discipline him and use a reward system that also subtly helps strengthen Levi's resilience and build his self-esteem.
Since I headcanon they both lay eggs (Barbatos is a salamander dragon Demon and Levi is a snake dragon) if Levi previously didn't go through that as an Angel (due to contrivances on my part) he would definitely be hiding that or in denial and Barbatos is observant as hell. That can lead to anywhere can't it ^^;
Well, now I'm embarrassed and idk how to sign off ;w; Oh wait, yes I do, Ballz! (inside joke)