Hello Tuna_28x,
Thanks for reaching out on the Apple Support. From your message it appears that you're unable to have a YouTube video enter full-screen mode when you double click on it.
I tested this on my iMac using an Apple Support video on YouTube, and was able to enter and exit full-screen mode in Safari. When you click on the full screen icon in the bottom right corner of the YouTube video window, does it enter and then exit full-screen mode? This will help isolate the issue. If that works as expected, work through these troubleshooting steps:
1 - Quit all apps. If an app will not quit, follow these steps to force it to quit: How to force an app to quit on your Mac.
2 - Restart your Mac: Go to the Apple menu in the top left corner of your screen > Restart.
3 - Hold down the shift key on the left side of the keyboard as you click on the Safari app to launch it. This allows the app to bypass the last saved state for the app. When the app begins bouncing in the dock, you can release the shift key. Once Safari is up and running, see if there is any change when you try to view this Apple Support YouTube video: 10 helpful Apple Watch tips you should know - Apple Support - YouTube.
4 - If you're seeing the same results, restart in safe mode and test again: How to use safe mode on your Mac.
5 - If still occurring in safe mode you’ll need to create a new user, sign into that new user with your information, and test it out again. This article will show you how: How to test an issue in another user account on your Mac.
All the best.