AstuteGraphics plugin pack has a plugin called DirectPrefs, that has Constraint Lock option. Once enabled, it counter-matches the Constrain Angle set in general preferences, giving you the grid that is always orthogonal to a view, which makes arrow keys work orthogonal as well.

Sure it must work from the box.

I love the new option to rotate the artboard. It is especially useful when working on dielines with panels that are facing different directions.

Currently when using arrow keys for nudging an object, the directions remain relative to the unrotated artboard. Meaning if you rotate an artboard 180 degrees, the up arrow moves an object down on the screen and vice versa.

It would be useful to be able to set the arrow keys to work relative to the monitor and not the artboard. That way if it is necessary to turn the artboard 90 degrees, the left arrow would still move the object to the left relative to the monitor rather than moving that object "down".

I have the same request, I believe this is a major issue. Changing my entire working routines, shortcuts and tools -that I've used efficiently for years- in order to accommodate a new feature is not an option.
At the moment the feature works just for viewing. It's not helpful to work with as the controls are practically disconnected from the screen view. When using a rotated view, all the tools (nudge, align, zoom) should work as if the artwork is rotated too. Having the tools behave as if the rotation is 0° is not helpful at all, it's really time consuming, as it feels like a forced brain game every time.
I understand that those tools are tied with the document coordinates which probably can't be rotated, but there needs to be a workaround.

You can move the view with PageUp/PageDown and modifier keys: Ctrl to scroll horizontally instead of vertically, Alt to use smaller steps instead of large. These require two hands (unless you use the right one) though...

As for the view rotation... I’d propose to use Shift (I think it does nothing now but dings). Will it work for you?

Not sure if arrows keys should be modal for that, but that is my preference.

It can, but it still can’t do it automatically.
See, it is not the canvas that is rotating, but a 'camera' looking at it, a viewport. The axis is still at 0, and arrows work accordingly.

To do what you want, you should copy the angle of the view rotation, open Preferences: General and set the negative of the copied value to the Constrain Angle field. Turn on the grid to see if it 'straight' now.

I am considering this request as 'Allow Ai to counter-sync Constrain Angle with the rotation of the view' :)

Move view (<h> key) and rotate view (<shift><H> key) should also be operable with the arrow keys when one of these keys is pressed. This is how it works when moving objects.
This would be helpful for people with disabilities and users of graphics tablets, who can then place the keys on the graphics tablet keys.

Windows 10
Illustrator Version 25.3.1 (64 bit)
Using mouse and keyboard, no wacom tablet

When using the new Rotate View Tool, all alignment buttons and arrow keys also get flipped... Meaning if you rotate view, your alignment center top and bottom with actually center left and right. Also nudging with the arrow keys will move it up or down instead of left/right.