What do you mean by "doesn't work"? For example, if you click in the address bar and type hello, replacing the URL, and then press Ctrl+Z, I would expect the URL to be restored. That doesn't work for you?

Another user mentioned that in previous versions of Firefox they could open a new tab and press Ctrl+z in the blank address bar and text would appear in the address bar from the previous tab. That doesn't sound like a built-in feature, so we haven't figured out how that was possible. See: Why is text history not persistent between tabs anymore?

if I type a URL in the URL field, and then select it and cut it by mistake, or change it by mistake, and then click CTRL+Z to get it back - it used to give me the typed URL as it was - now it doesn't.

As I said in my question - I used all the common "medications" restarting the computer, refreshing the Firefox, re-installing Firefox - all in vain, didn't help.

In the example where you accidentally cut, you can paste to recover what you cut. However, in the example where you "change it by mistake" I'm not sure I understand what you were changing it from.

If I type in the address bar of the current tab and press Ctrl+z, I get the URL of the current page back.

If I open a new tab, which has a blank address bar, type anything and use Ctrl+z, it goes back to blank.

What was it doing before in those two cases?

I know that I can paste a "cut", but I don't feel comfortable, and it doesn't solve the rest of the problem.

To make the issue clear, take an example. this is an orig. URL:

https://www.cnbc.com/2017/08/03/last-year-trump-thought-stocks-were-a-big-bubble-not-anymore.html

by mistake I change it to:

https://www.cnbc.com/2017/08/mp-thought-stocks-were-a-big-bubble-not-anymore.html

Before the problem rose I recovered the URL by CTRL-Z (undo).

Now I have to re-google it.