In Arena, it can clearly be seen rising in the west and setting in the east.

I never noticed the Sun in the sky at all in Daggerfall, presumably because of the constant clouds covering most of the sky all day long. But I just loaded a save, loitered until between 5 PM and 6 PM, and caught a brief glimpse of the setting Sun in the northwest sky, but then it vanished-- again, presumably because of the clouds. So it would seem that the Sun rises in the east and sets in the west in Daggerfall, with the season of the year perhaps affecting whether it rises and sets north or south of due east and west.

In TES3:Morrowind and TES4:Oblivion, the Sun can be seen rising to the east and setting to the west.

I don't remember from TES5:Skyrim, but from the trend shown above, I'd guess that it rises in the east and sets in the west.

One of the Notes at the end of https://en.uesp.net/wiki/Lore:Sun says that

Originally, the Sun was meant to set in the east and rise in the west, and the directions of east and west were intended to be reversed across the board in the Elder Scrolls setting. Remnants of this design can be found all throughout Arena. Ultimately this was inconsistent throughout the game's design, and was abandoned for future titles.[UOL 3] Dawn's light rising in the west is mentioned in The Legend of Lovers Lament from Daggerfall, however.[77]

The inconsistency in Arena that is referred to must mean the orientation of east and west, because on the player's compass and on the map they are oriented as we know them to be (east to the right and west to the left), but when handing out quests the city rulers often use the terms backwards from what we know-- that is, they might say that a particular dungeon you need to go to lies to the east, northeast, or southeast of the city, but when you pull up your map the dungeon will actually be to the west, northwest, or southwest of the city (according to how east and west appear on the compass). Yet I believe there is a screenshot in either the game manual or player's guide showing a compass with east to the left and west to the right. So this might be the inconsistency referred to.

It would seem that they scrapped this idea in Daggerfall, aside from whatever had been written in the lore books, so there is also some inconsistency in Daggerfall. However, that might be due to many lore books reportedly having been written by the playtesters-- that is, maybe the devs had changed how the Sun is depicted rising and setting in the game, but the playtesters were writing based on their familiarity with Arena? And I'm wondering if perhaps the devs decided to use clouds to obscure the sky such that the Sun's disc can hardly ever be seen in the game, to help minimize any confusion over this issue?