Have you tried Kingdom Come : Deliverance ?
I'd be glad to hear your opinion about immersion in this game. I'm sure you would like it ! Except maybe for combats, it's probably one of the most immersive open world game I've ever played... But TBH except this one i'm usually not a fan of OW games because despite being very complex, these universes always have A LOT of filler content that really annoys me and just break my enjoyment and my immersion after some time (bandit camps, hunting spots, treasures, monster's den...).
Yeah. I've played Kingdom come, and it shines in some of the physically immersive things that I've tried to outline here. The world at times feels "lived in", is detailed, aiming for historical accuracy, has a kinda large area to adventure in, with wilderness areas(bit small for my tastes), where you can actually get lost, or at least disoriented in, and traveling in the night feels different and is markedly more dangerous/difficult. Because of this stealth/thievery mechanics were enjoyable at times and I really liked exploring the surroundings(until I got bored with the repetetive sidequests). The combat was a bit of a mess, with overemphasis on the unblockable counter strikes, but it had its gritty hard hitting moments. At least they were aiming for something new. But yes, in this physical sense the game does many things right.
The world still often felt static, especially after you reach the point where you're sent to investigate the raid on the horse farm. From then on you sort of go mostly solo sleuthing, despite sometimes shortly teaming up with various (mostly disagreeable and ridiculously inept) people and participating in few small scale skirmishes with other soldiers. This lack of belonging to a group of adventurers, or to a otherwise closely knit community ingame, greatly diminishes any sense of immersion for me, partly by emphasising the sense that you're alone the only active person in the world. Even though you're often on the clock while completing the main quests, and there's some engaging rng and sidequests(apart from the filler content) to make it feel like it's just not you that's active in the world, you still start to progressively feel like everyone in the world(especially the nobles that send you to increasingly dangerous missions) is just waiting for you to do things.
But the game really comes apart at the seams for me due to the bad (main) storyline/writing. While I appreciated the detailed world building, the plot and the writing felt unimmersive, ahistoric and downright repulsive at times. Instead of a game aiming for realistic depiction of feodal era, it often looked/felt more like a modern nationalist fantasy of medieval times: more like a modern story of unified nation(apart from the usual roster of traitors) coming together to fend of exceptionally foul foreign invaders. You're also, for the most time, spectacularly exempt from(and unaware) the rigid social hierarchy and internal strifes of feodal times, which is not just unimmersive, but also a lost opportunity in storytelling. It would have been way more interesting, if the main protagonist hadn't been so thoroughly uprooted from his life as a commoner into a jumped up noble/soldier/official and plot railroaded into fighting in the war in the introductory chapter. The game also had some homophobic(rather nasty use of pseudo-Freudian "seduction theory" employed for gay bashing) elements/undertones in it. This all made it feel like the devs were less interested in immersing the player to a realistic tale from the feodal ages, than in immersing players in right-wing culture wars.