Replace the desktop video path with OWE

The desktop background no longer plays videos. OWE owns video
backgrounds, and the shell layer stays empty behind one. The shell keeps
stills, which OWE hands back to it.

Remove the desktop video pause plumbing that only existed to stop an
unseen player: the lock, idle, and battery service lookups, the
per-output fullscreen check, the first-screen audio opt-in, and the audio
output in BackgroundVideo. The lock screen keeps its own silent playback.

Update the background tests, the manual, and the package note.

install/omarchy-base.packages

@@ -107,8 +107,8 @@ python-poetry-core
 ttfx
 qemu-user-static-binfmt
 qrencode
-# TODO: add owe-wallpaper-engine here once it is packaged. The shell yields
-# video backgrounds to it while its daemon runs.
+# TODO: add owe-wallpaper-engine here once it is packaged. The shell keeps
+# stills and the lock screen, and OWE owns desktop video backgrounds.
 qt6-imageformats
 qt6-multimedia
 qt6-multimedia-ffmpeg