Note: other than FF, you can also trigger PiP (edit: on Safari) on a YouTube video by double-right-clicking on the video element OR long pressing on the speaker icon on the tab/address bar.
Neither of these worked for me. Chrome 83 on Win 10.
It was then locked away behind YouTube Premium, and now YouTube (non-premium) occasionally bugs you to pay for the premium when you try switching to another app so that you can continue playback.
I've been using pipifier for this - especially for Netflix, didn't know about this until now - thanks
Not sure if it's possible to get a browser-based YouTube video to go PiP on iOS Safari.
You should then see the browser contextual menu with 'Picture-in-picture' in the list of options.