When I enter full screen I can click on the name of the YouTube video and access the video, also save it in “Watch later” (if my YouTube account is open).
First I open the page with the video.
Then I double click on the video or click on the enlarge screen button.
Then, with the full screen, click on the name of the video.
What will happen is that it will open a new tab that directs to the video on youtube.
Sorry, right now I can’t give you the catch.