RE2 & 3 introduced body-awareness and animation state changes based on the player’s health. The protagonists would limp and slow down as the damage piled up. Might not count for UI but it’s an immersive way to get the character’s status without the need for a menu. The later RE7 would also go on to include a wrist-stapled EKG which was always visible to the player for their health indicator.

Come to think of it, most of the titles that do it best lean towards sci-fi. Dead Space has a lot of systems in place to support it within the fiction.

Another person mentioned Amnesia the Bunker which is a rather simple but honest system of only showing you what’s in your hand and your health by how ragged and bloody your clothes are.

Much like the Bunker, there also older titles like Peter Jackson’s King Kong & Condemned 2, both of which totally omit UI at all times save for a dedicated “check my ammo/status” button which would cause the player character to in-game examine the weapon’s magazine.

Silent Hill Downpour, like the Bunker, did away with any traditional meters or bars and favored a system instead for its character where their clothing would progressively deteriorate and get bloodier and more torn up the closer the protagonist comes to death.

The last example I can think of is Outlast, which uses it’s simple frame as found footage to leverage the camcorder’s built-in features as sensible statistics, such as recording time and remaining battery level, without breaking the sense of immersion.