Could someone recommend me mangas where the two characters are a couple, they fight and split up (and I mean an actual fight, not a peaceful breakup), then either one of them vanishes from the story completely while the other moves on to another partner and ends up happy, or they both stay in the story and find their own partners and end up happy?
Something like Lily Love and its sequel and the whole thing that happened with Ploy in those two works,
Ring My Bell is pretty much that (the fight part is a bit delayed but it's there too)
Wish You Were Gone if you don't mind the previous partner being male and him not disappearing immediately. The advice on it seems to be to switch between the fan translation and Tapas' expired-licence official translation whenever one of them gets too confusing.
There are breakups (including a messy one with a whole season of angsty fallout from it), broken hearts, moving on and a happy ending in this webcomic, but I don't remember if there's a single chain of events exactly as you describe it present.
Good luck hunting down a complete and readable translation if you want it in English, though (for reference, it's 150 chapters long). There was one on Youtube, but the translator's channel appears to have been banned.
Additionally, here's a minor spoiler to explain a side plot that the story starts with but that isn't conveyed well (either it's lost in translation or a cultural reference that went over my head): there's systemic bullying/hazing with the freshmen being regularly herded by older students into a hall and forced to waste time sitting there, that's bizzarely tolerated by everyone and which the main chracter wants to avoid.
