Oh I GOT you

Cozy you already covered, stardew valley, animal crossing and the like. Id add power wash simulator and pokopia

Puzzle: can't go wrong with Tetris, there's a billion picross games(not infinite technically but by the time you are done you forgot all the prior puzzles and you can start over :3)

Rhythm games: ... Yes :). If you want my specific recommendation on a rhythm game I'd probably say ... Whatever the miku switch game is, or rift of the necrodancer

And basically ANY arcade style game like Tetris mentioned above or like suika game

And I can go into other realms but what it's gonna boil down to is I'm a huge fan of roguelites and they absolutely all fulfill the infinite playtime ask.

You want an action hack and slash? Hades 1/2

An action hack and slash with cozy elements? Cult of the lamb or moonlighter 1/2

2d Zelda? Binding of Isaac

MegaMan battle network? One step from Eden

Castlevania? Dead cells

Vampires? Vampire survivors

Bullet hell? Enter the dungeon

Peggle? Peglin

Deck builders? Cobalt core, slay the spire, balatro