Bit of a late response, and maybe you already know of it, but if you or anyone in the future going through this thread are still looking for that kind of manga, might I suggest Wanna go out?/How Do We Relationship?
Oh yes that's one of my favorites, but that one does start with them immediately going out rather than there being a lead up to them getting together that then gets undercut when they realize things aren't as compatible as they initially thought, How Do We Relationship has no build up so them breaking up is more expected. But ye, it's definitely the closest to that idea by a mile, don't recall anything else that comes close, even just breaking up in a story is super rare.
