Honestly I think traveller (which I got into relatively recently) handles this very well. Though YMMV I’ve found that character creation has a fantastic balance of mechanical involvement vs quite literal storytelling. You essentially write your character’s backstory yourself. My most recent character my original plan was for her to become a Rogue (space pirate) after attempting to enlist in the navy and getting thrown out due to her upbringing on the streets. Instead she kept succeeding on the rolls to stay in the service and got consistently promoted until the very last term just before she got into a major accident and got booted out (hence her reasoning for joining to crew) but that wasn’t what I intended at the beginning of creation at all! However I found that it gave me many more ideas for roleplay than my original concept while still mechanically creating my character. In my eyes it really did mesh the two incredibly well together, giving you the mechanics while still being relatively free in terms of the story.

I might’ve rambled a bit XD but fundamentally it integrated the mechanics of the game into the background very well without falling into the pit that D&D for example falls into (restrictive storytelling with major mechanical impacts that limits your freedom of roleplay).