Did you hit the F11 key to get out of full screen mode? Attached is what youtube opened as here - do you have Firefox set to open with last tab visited? What url is showing that black screen (which is full screen mode)? Firefox doesn't alter any website it opens and has nothing to do with youtube.

Could you test in Firefox's Troubleshoot Mode? In that mode, Firefox temporarily deactivates extensions, hardware acceleration, any userChrome.css/userContent.css files, and some other advanced features to help you assess whether these are causing the problem.

If Firefox is running:

You can restart Firefox in Troubleshoot Mode using either:

• "3-bar" menu button > Help > Troubleshoot Mode...
• (menu bar) Help menu > Troubleshoot Mode...

and OK the restart. A small dialog should appear. Click the Open button.

If Firefox is not running:

Hold down the Shift key when starting Firefox. (On Mac, hold down the option/alt key instead of the Shift key.) A small dialog should appear. Click the Open button.

Note: Don't use the Refresh without first reviewing this article to understand what will be deleted: Refresh Firefox - reset add-ons and settings.

Any improvement?

Ref. Diagnose Firefox issues using Troubleshoot Mode

I launched Firefox in troubleshooting mode and even reset the settings, but it didn't help

This has nothing to do with Firefox. This is YouTube doing A/B testing. It's been slowly rolling out of the past year. You can try creating a new profile to check if it works there but no guarantees. Once you've been hit with this, that's it. You can switch browsers but eventually it'll start to affect those too.

But why is it only on this browser, when the others have the old interface? I also asked other people and they also only have it changed on Firefox.

These types of changes are controlled server side by Google. It is just a coincidence that it affects Firefox and not any other browser but like I said you can switch browsers but eventually it'll start to affect those too.