I know nothing about the detailed technical differences between X11 and Wayland but with Hyprland for me the PIP is working as expected so I assume its not just a Wayland issue but specific to the window manager you are using? Maybe somebody else can explain?

As far as I know, there are multiple Wayland implementations. Which is also not good because it creates fragmentation and potential inconsistencies (some subtle differences in behavior, differences in bugs, etc). Maybe Hyprland solves the issue, but I don't want to use this DE just because it solves this particular issue. I have tons of other needs and preferences.

Isn't that usually how it goes? Wayland is a million little optional protocols, which in the abstract is a lovely idea but in practice means which things work depends on which grab-bag of features your compositor supports.

I think in Hyprland it just works because floating windows stay on top by definition.

Gnome has a "Always on Top" toggle for each window. I imagine there's a protocol for an application to set it by default but the OP's window manager might not implement it or there might be an incompatibility.