Looking for a game where reading an immersive in-game manual is one of the main gameplay aspects

I love Elite but I don't think it's what OP is asking for

https://store.steampowered.com/app/4209010/Lakehopper/

Great games, but that's more of just flavor text than a _manual_ type situation.

I love Zachtronics games that have been recommended a few times already. But for a different genre...

Ni no kuni is a RPG that was kind of that, with a big (originally physical) book of magic. But since it's been remade on many platforms as a digital download, the book is there in a rather boring pdf reader-like UI and has been made a bit less useful.

It's still rather charming having this in-universe codex-like book listing gameplay elements, items, recipes, bestiary, and bits of lore about the world (and some pages just telling random fables about whatever). Nowhere near required reading for the game though, just occasionally useful.

Ostranauts?

Its a space salvage game with a good atmosphere

Keep talking and nobody explodes.

One player(s) has the bomb disposal manual and the other has the game controls to defuse the bomb.

Still There

If by "in-game manual" you mean one that's part of the game world (not necessarily displayed on a computer screen) check out the classic Infocom adventures. For example, Border Zone came with a printed terrain map and tourist guide, and Sherlock and The Witness came with newspapers, among other things.

Tunic?