I am testing out how to move a widget from one widget area to another.
Test 1
using the up and down move arrows.

It goes to the bottom of the widget area. I am not able to use the down arrow to move it to the next widget area.
Test 2
Using the 3 dot drop down menu. Move to.

That does not at all work. I see a blue line but I do not know how it is associated with the Move to action.
I am not able to use the Move to action.
I agree we need a way to move a block to a different area without using drag and drop.
_Move To_ is working, albeit it's confusing. If you select _Move To_ you can then use Tab and Shift+Tab to move the blue cursor around.
I do believe this might be the best option.
Adding a submenu to the Move To option. Something similar to this, just prettier.

@mapk
So one way to do this is just cutting and pasting the block into another area like so:

I'm okay using "Move to" but it should NOT change the behavior from the post editor. The behaviors should remain the same with an added "Move to" selected widget area.
I'm finding it very difficult to use the keyboard to jump between widget areas. If this was refined, the "Move to" could work much better. I'll create an issue around using the keyboard to jump between areas.
So there is a Move to option in the post editor as well. Never really used it. It is a bit confusing and cumbersome to use.
Adding a cut & paste and drag of widgets between widget areas will help.
https://github.com/WordPress/gutenberg/issues/25243
Related: #25911
I think we have a good way forward by implementing these as you mention, @paaljoachim.
Adding a cut & paste and drag of widgets between widget areas will help.
Let's get this to dev. :)
What's the thing that Needs Dev here? Cut, copy, paste should work, and drag and drop is tracked by other (now closed) issues.
@talldan, the Move To option just doesn't seem to work when trying to move one block/widget from one area to another. Here's a video of me trying the Move To without any success. I tried with a both a mouse and using the keyboard. I couldn't get it to happen.

When I'm inside a widget area, I can't easily switch to another widget area using the keyboard. I did happen to see a grey line in between widget areas appear which was really weird.

And in other cases,
Okay, tried this again, and there seems to be a really confusing requirement that a Move To needs to have two blocks in another area to actually move the new block between? Here's another video of me trying again. It wasn't consistent after clicking "Move To" what got highlighted. It would NOT move the block until I selected a block in the other area.

I should be able to select a widget area and drop the block inside it, at the bottom, without having to click into the widget area.
For myself this action is extremely confusing. The Move To button feels to have no action or tell as to what your next step is.
I did like @paaljoachim idea of giving the moveto a direct action menu which is the current list of sidebars and widgets/blocks.
It is a bit difficult to understand, it was mostly implemented for screenreader users IIRC and there are some audible instructions.
Anyway, my understanding is it primarily works using arrow keys, up/down for moving up and down, left/right for un-nesting/nesting. Right key works when the insertion line is above the block you want to nest into.
There was a design somewhere showing some visible instructions for using move to mode. @paaljoachim do you remember seeing that? I couldn't find it 馃槃
Hey Dan @talldan
I am not sure if I have seen any design of the Move to mode. As I had not noticed that the mode even existed earlier as I went and added the action menu mockup further above which was mentioned by @garretthyder.
Ah, I was thinking of this issue - https://github.com/WordPress/gutenberg/issues/25126