DuckDucking it, I couldn't find a solution, but I hope someone can tell me there is.
Outside of things like this (and finding the right screen recording program) I didn't really notice a difference.
Step 1: Right click an open Picture-in-Picture window. In the context menu, select "More Actions" -> "Configure Special Window Settings...". This will populate most of the window settings for you.
Step 2: Click "Add Property..." and select "Window title". The newly added row's text field should read "Picture-in-Picture". Change the dropdown option from "Unimportant" to "Exact Match". (All PiP windows in Firefox use this title and by making it Exact Match the rule shouldn't affect any other Firefox windows.)
Step 3: Click "Add Property..." again and this time select "Keep above other windows". The dropdown in the newly added row should be set to "Apply Initially". Select the "Yes" radio button if it isn't already. (As a note, I think that didn't work for me as I have it set to "Force" rather than "Apply Initially")
Step 4: Click "OK". That's it. No more manually setting Keep Above every time you open a PiP.
Since doing the above it's just worked without issue, though it was annoying that it was broken in the first place.
https://old.reddit.com/r/kde/comments/osjt3p/firefox_wayland...