I figure that Marina showed up in my dream solely because, as I was falling asleep, I distinctly remember pondering that she is One Million Times Bigger than usual in her boss fight compared to her actual model, and that that makes sense from a game-playing standpoint but not so much in the world itself XD I also wondered how Eight managed to like... un-grayscale themself, when you start ramming the button n shit after everything went white. Pearl calls it their vibe iirc, but like... how does it work precisely🤔🤔
Oooh okay time to pull out the ol' Splatoon lore muscles. Ok so the first thing to note is that everything in the Orderverse happens digitally. It was originally concieved under the name of "Project Memverse" by Marina as a VR program to return the Mem Cakes (memories forcibly removed from sanitized Octolings, who would normally have then had to go through the Octo Expansion stages to get them back) from Kamabo Co. to their original owners, and reverse the effects of Sanitization as a whole. However, an AI Marina designed for it essentially went rogue and found out that if people had a certain type of phone, it could get into them and basically draw them in. On the outside, this appears as them being unfocused, somewhat lazy, and dazed for long periods of time, as their mind is trapped in the Orderverse. This is the preliminary stage to a process called "grayscaling", in which (iirc) all originality is wiped from that person's mind and everyone whose mind is accessible by the AI now running the Orderverse is forcibly made homogenous to establish order. It essentially weakens one's mind, and once enough people are in that weakened state, it forces a hivemind onto everyone to try and make a world where indipendent thought is impossible.
Thus the reason Marina's so big in her bossfight is mostly because it's a virtual space, and while that AI is controlling her, it can do whatever it wants to the model she's using for herself. It does a similar thing to itself, too.
As for the vibe check thing, what happens here is that this AI- known at the time as Overlorder- fights Agent 8 to a standstill in their bossfight, and manages to activate the full-fledged Grayscaling process (the hivemind part) on everyone in both Inkopolis and the Splatlands that it has access to. This basically KO's Agent 8. The little minigame rhythm game (some people button spam‚ but the game encourages you to go on beat!) is a little cloudy on what exactly it is- I'd say it's a bit like the determination mechanic in Undertale's true pacifist final boss that refuses to let you die. It presents simultaneously as Agent 8's heartbeat and the beat to Ebb & Flow, so in theory it's Agent 8's will and resistance against Overlorder that makes them push themselves to get up again and resist the Grayscaling process. This cutscene seems to present Ebb & Flow as narratively quite similar to the Calamari Inkantation. They both inspire Agent 8 to resist against control and push past their limits, which is important- Ebb & Flow‚ the original Octo Expansion final boss track‚ becomes almost like a second "heavenly melody" here, one that liberates people from Overlorder's control the way the Calamari Inkantation inspired Octarians to seek the surface world. Agent 8 associates that song with achieving the surface life they dreamed of and saving countless other Octolings from potentially sharing the same fate as the ones down in the metro‚ and thus it is that song that reminds them that they can do that again. Or at least, that's my interpretation, anyway. All the wiki says is that "The player "brings back the beat" in a small rhythm minigame and wakes up Agent 8." So it's a little up to interpretation, but that's more or less the gist of it. In a way, it's like the game reminding you of the old gamer mantra "if it can bleed it can die", and going hey we're not losing that easily.
So yeah that's about what I can say! Inkipedia is a really good resource if you wanna know more, so check it out if you like, but a lot of my evidence for this comes mostly from just having played the games haha.