Proper system-wide picture-in-picture support (currently only works in Firefox and not fully)

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Feature request

Which Nextcloud Version are you currently using: Current cloud.nc

Is your feature request related to a problem? Please describe.
Google Meet for example offers a really nice picture-in-picture mode. (Since they have the luxury of owning Chrome as well, it even works automatically when navigating away from Meet as the current tab.)

• This particular mode only works in Webkit-based browsers, but Firefox already has its own custom picture-in-picture version we support – with some small issues: https://github.com/nextcloud/spreed/issues/4862 & https://github.com/nextcloud/spreed/issues/4674

Describe the solution you'd like
It would be nice if we use the Picture-in-Picture API as well, so supported browsers (Webkit based like Chrome, Edge, Safari, Opera, etc.) would have a nice picture-in-picture as well.
https://developer.mozilla.org/en-US/docs/Web/API/Picture-in-Picture_API
It could simply be an entry in an action menu to start it off, and that entry would only be there if the API can be used. (If possible in Firefox as well, clicking on that button could start picture-in-picture on the promoted video element?)

Additional context
This is how Google Meet handles it: https://support.google.com/meet/answer/13665919?hl=en

Start by reading the Picture-in-Picture API documentation and locating the call action menu and promoted video element in the Talk interface. Add an available action for supported browsers, then verify that it starts Picture-in-Picture and that the action is absent when the API cannot be used, including Firefox behavior where applicable.