If you use KDE, you can work around this because of the powerful feature set the window manager has for setting custom window behavior.
1. Right click the PIP window and then click "More Actions-> Special Window Settings".
2. On the window that pops up, click "Add Property", and add "Window title". Change the drop-down from "Unimportant" to "Exact match" (this works on Firefox because the window title is always "Picture-in-Picture", you might have to do something slightly different on Chrome if it does something different).
3. Click "Add Property" again, add "Keep above other windows", change the drop-down to "Force", and change the radio button to "Yes".
4. From now on, all PIP windows will show up on top of other windows.
It would definitely be nicer if there was some sort of "always on top" permission that applications could request, but it's not too bad.
For Chrome it's "Picture in picture"
Wow, I guess Linux is only free if you don't value your time.
Not too bad? A hidden procedure with ten clicks, which the user has to repeat for each web browser. And it may break at any time if the browser changes some details. Or if KDE changes. And it's specific to KDE, with no alternatives in most Wayland WMs.
All that for _one_ feature which works out-of-the-box with Xorg, and which Wayland removed for security reasons. From what I've seen, sharing the screen is another common feature which was broken with Wayland and is still painful.
I don't think Wayland's security model is very relevant to me since I have faith in Debian for filtering out rogue applications. So I have to reason to drop my smooth UX for a world of "not too bad" workarounds.