Edit
It's impossible. Picture-in-picture mode is a built-in browser and there are no APIs to customize

If you are using MAC OS, you can try IINA program which has rotation feature.
IINA player: https://iina.io/
add-on "Open In IINA" : https://addons.mozilla.org/en-US/firefox/addon/open-in-iina-x/

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Hi. Thanks for the feedback.
What do you mean latest update on Youtube? I tested it but the button still show.
If you are installing the add-on for the first time, you need to refresh the page