Try the following:
- Start or load a game in DFU.
- Press the "Activate Cursor" key (default: ENTER).
- Try to turn left or right using the keyboard (default: LEFT or RIGHT).
What happens? Well, when I do it, nothing happens, the keys simply don't work, remapping to other keys is possible, but doesn't achieve anything.
In classic Daggerfall, it works.

Looks like a DFU bug to me, but it may also be a design decision of the DFU developers to not map the LEFT and RIGHT keys to any action. In the second case I'd be interested in learning the rationale behind this decision.
Or does it work for anyone?

DFU only includes the mouselook controls, which were also available in classic Daggerfall.

The mouse cursor controls have not been implemented and I do not believe there is a plan to do so.

Btw, pressing Enter to activate cursor mode did the exact same thing in classic Daggerfall. The function is to switch to using the mouse-pointer to click stuff while using mouselook controls. It honestly have little use in Daggerfall Unity unless you use the big HUD and click the buttons there instead of using the key bindings.

Thanks - it's what I guessed (and why I didn't simply call it a "bug").

I'm a Daggerfall player "of the first hour" and used to playing Daggerfall in the Daggerfall, not in the DFU way. This includes controlling movement with the keyboard, and using the mouse for fighting, acting (grabbing, talking, ...) and clicking the icons on the bottom of the screen. Without being able to turn with the keyboard, I can't play DFU in the same way as Daggerfall anymore (and it's why I keep saying that DFU does not have the full functionality of Daggerfall).
On the other hand, I do appreciate and like DFU, and would like to continue playing Daggerfall in DFU. One way (and I'm sure you would recommend it) is to play in "fullscreen" mode and learn all the keyboard controls (most of which were present in Daggerfall, too). I'm afraid I'm a bit too old and too used to my old way to play Daggerfall to familiarise myself with the "new way".

I think I found a compromise I can live with: Disable fullscreen mode (so that the icons are visible), use the keyboard for moving forward, backward and sideways, and the mouse for turning and looking up / down (which is convenient), disable swinging (attack by clicking the mouse), and press ENTER when I want to access the icons (I may learn to replace this with key strokes step-by-step). It feels more awkward than my old way of playing, but it looks like I can live with it. Otherwise I can always return to classic Daggerfall.
Nevertheless, I find it difficult to understand why keyboard turning was left out when implementing Daggerfall functionality in DFU when so many other things (among them many I could easily live without) were included.

Funny, I never used that control scheme, even back in the 90s. I just switched it to mouselook back then so I never realized people were actually using the mouse controls. For me, the setup in DFU is pretty much exactly how I always played it.

Awkward as it might seem today, using the cursor-based movement scheme was the best way to sneak (without perma-crouching, which looks absurd), as well as making interaction with the environment a little less fiddly. Not sure if the controller support in Unity allows for fine-grain "analog" movement that would make that irrelevant for controller-users, but even if so, that wouldn't help the keyboard-and-mouse users.

Not sure what you mean by fiddly? You looked at suff and left clicked to interact with it?

I do not think I ever bothered sneaking, seeing as you had to be damn lucky to not just wander into the enemies sight when when walking through a door or atound a corner.

Having to center not just the mouse cursor, but your whole view on the item or environmental feature you're trying to interact with. I'm sure you get used to it after a while, but if you're used to using cursor interaction outside of combat, it can be annoying. Depending on the character you're playing and the specific current circumstances, a bit of sneaking now and then is just good RP. :)

In unmodded DF, sneaking is literally just moving slowly. There's no special button for it. Since crouching causes the character to move more slowly, that's presumably how a lot of players (i.e., most who played with mouselook on, which I do imagine was probably the majority by the early '00s, let alone much later) accomplished it, and that's likely why later Bethesda games went with the more simplistic "crouch to enter sneak/steal mode" mechanic.

Also, is my memory failing me, or wasn't there a crouch toggle in the unmodded game? Or are you just saying that DFU added a button that puts you in "sneak mode" without having to crouch, AND that one can set it to either "hold to sneak" or "toggle sneaking"?

Default : D

Sneak and Crouch are two separate actions, in DFU only perhaps I have not played the original Daggerfall in MANY years so I actually don't recall. I've only played DFU for the last few years or so. I also played Daggerfall at its original release in the 90s so the chance I can remember that well is really low. I'm getting old :)

There is a "toggle sneak" in the DFU launcher advanced->gameplay options you can enable or disable.

The default keys for these actions are:
L Ctrl: Crouch
L Alt: Sneak

Those can be seen in the game proper in the ESC->Controls menu.

I have "Sneak" backstabbed many an enemy without crouching in DFU, you just move really slow in "sneak" mode.

I think so far the only thing I've really used crouch for is to get into a half-height hole in a wall. As to whether or not using both crouch and sneak at the same time will give you a better chance of not being detected in DFU, I have no idea.

No, as long you are moving at less than half speed it is the same. So crouching is only really useful for jumping through holes. And there is a mod for combining the two together.