That is, they are not just frozen in place, or forever doomed to wander back in forth in a single location. Instead they get up in the morning, do 'stuff' during the day, and then go to bed at night (most of them in any case). The first game where I encountered this was Oblivion and found it did absolute wonders for immersion. So much so that when I returned to Morrowind some time later, I found the observation that most NPCs are frozen in place to be really distracting and immersion-breaking. Though perhaps it only bugged me as much because of the obvious parallels with Oblivion.

Are there more examples of games that have these kind of NPCs, apart from Skyrim of course?

The NPCs in Piranha Bytes games like Gothic, Risen, and Elex have the same kind of cycles.

Kingdom Come Deliverance

Ultima series, starting with Ultima 5. Note that, until Ultima 6, their state doesn't persist, so dead townspeople come back to life when you leave, but still have lives.

Ultima 7 I remember there being a hidden room where the dead went. Ah, happy days with that game.

OP:
As for npcs being active, I think that is a bit overplayed, sure they may go to work, but medieval times (quite a bit of fantasy) they didn’t move about much. Not like today where going for a pee requires jumping in the car.

Party based npcs are the worst thing. Get in my way, need to talk be fed directed. Hate party based games. If I wanted.l a baby would have one! Other npcs are just there to increase your archery skill!

Stardew Valley? Example of a schedule that changes by day, by season and by weather (rain vs dry).

OP,
The Way of the Samurai games have extremely detailed NPC lives, and are pretty interesting games where you can do just about anything you feel like doing.
Way of the Samurai 3 + 4 are also available on GOG
https://www.gog.com/game/way_of_the_samurai_3
https://www.gog.com/game/way_of_the_samurai_4



Alternately, have you looked into old MUD-style games?

Ultima 7 also had a nice cheater's room, only reachable if you cheat, where Lord British accuses you of cheating and casts Armageddon; if you then talk to him, he spouts procedurally generated nonsense. It's too bad Ultima 7 was a terrible game.

Party based NPCs are only a problem in games that keep track of their position and use it in collision detection. In Ultima 6, for example, if you're not in combat or solo mode your companions will follow you nicely and in a way that doesn't impede your movement. In earlier Ultima games, and in Wizardry games, and in Might and Magic games, and in nearly all JRPGs (at least Dragon Quest 2-9 and Final Fantasy 1-10 (DQ1 excluded due to lacking party members)) your party members either don't exist or are not solid outside of combat and cutscenes.

By the way, some Dragon Quest games, 3 being the best example (though there's some in 4, 5, maybe 8 and 9), have day-night cycles, and many NPCs are in diffierent places depending on whether it's day or night; DQ3 even has a store that you can rob during the night. (DQ1 and 2 don't have a day-night cycle, and DQ6 and 7 only have night-time during scripted events instead of a regular cycle.)

New Vegas, nodiscuss.

Yeah. Bethesda made a big deal about it with Oblvion, and carried that on through all their games. Obsidian obviously did as well, using the same engine. Piranha Bytes was another good example. Important to note though it depends on the NPC how involved this is, some of them (like bartenders or whatever) often just stand in one spot all day and sleep in a nearby bed at night.

In vegas mostly (not all) NPC's have their own backstories OwO

The Legend of Zelda: Majora's Mask also claims this, and it does it pretty well as far as the town of Clock Town is concerned. It's also interesting that the world will end if you take too long (so you don't have townspeople doing the exact same thing each day), but once you get past the first cycle you can easily reset time whenever you need to (at the cost of losing your consumables and dungeon progress).

Shenmue. Much to the detriment of the series.

Well, we will have to disagree there. I can’t stand jrpgs (or vns etc). Ultima 7 however I went through 2 or 3 times with serpents isle, still have scanned maps I did back then. One of the classics. The others in the ultima series also (well 7 and below anyways). Never played the online one.
Npcs are always bad, they all have one or more annoying feature. A need to talk all the time, get in the way, need upkeep. Etc.
First thing to do in dragons dogma for instance is push the pawn off a cliff!