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.

test/shell.d/video-background-test.sh

@@ -33,7 +33,7 @@ assert(
     videoQml.includes('autoPlay: root.playbackEnabled') &&
     videoQml.includes('fillMode: VideoOutput.PreserveAspectCrop') &&
     /imageUrl: path && !Util\.isVideoPath\(path\) \? Util\.fileUrl\(path\) \+ \(version \? "\?v=" \+ version : ""\) : ""/.test(mediaQml) &&
-    /videoUrl: path && Util\.isVideoPath\(path\) \? Util\.fileUrl\(path\) : ""/.test(mediaQml),
+    /videoUrl: path && Util\.isVideoPath\(path\) && videoEnabled \? Util\.fileUrl\(path\) : ""/.test(mediaQml),
   'background media plays aspect-cropped videos on a loop, and hands each loader only its own kind of file'
 )
 assert(
@@ -62,16 +62,12 @@ assert(
 )
 assert(
   !/^\s*Video\s*\{/m.test(videoQml) &&
-    /property bool audioEnabled: false/.test(videoQml) &&
-    /property bool audioEnabled: false/.test(mediaQml) &&
-    /active: root\.audioEnabled && player\.hasAudio/.test(videoQml) &&
-    /audioOutput: audioLoader\.item/.test(videoQml) &&
-    /muted: root\.priming \|\| !root\.playbackEnabled/.test(videoQml) &&
-    /property: "audioEnabled"\s*\n\s*value: root\.audioEnabled/.test(mediaQml) &&
-    /firstScreen: Quickshell\.screens\.length > 0\s*\n\s*&& String\(Quickshell\.screens\[0\]\.name/.test(backgroundQml) &&
-    backgroundQml.includes('audioEnabled: panel.firstScreen') &&
+    !videoQml.includes('AudioOutput {') &&
+    !videoQml.includes('audioOutput:') &&
+    !mediaQml.includes('audioEnabled') &&
+    !backgroundQml.includes('audioEnabled') &&
     !lockQml.includes('audioEnabled'),
-  'a sound track plays from the first monitor only, a silent file builds no audio output, and the lock stays quiet'
+  'playback is silent everywhere, so no audio output or audio client is built'
 )
 assert(
   /property: "mediaSource"[\s\S]*?when: videoLoader\.item !== null && Util\.isVideoPath\(root\.path\)\s*\n\s*restoreMode: Binding\.RestoreNone/.test(mediaQml) &&
@@ -88,13 +84,20 @@ assert(
 )
 assert(backgroundQml.includes('BackgroundMedia {') && lockQml.includes('BackgroundMedia {'), 'desktop and lock screen share video-capable media rendering')
 assert(
-  backgroundQml.includes('property bool oweActive: false') &&
-    backgroundQml.includes('/owe/owed.sock') &&
-    /deferVideo: root\.oweActive/.test(backgroundQml) &&
-    /property bool deferVideo: false/.test(mediaQml) &&
-    /active: root\.path !== "" && root\.video && !root\.reloading && !root\.deferVideo/.test(mediaQml) &&
-    !lockQml.includes('deferVideo'),
-  'the desktop yields video backgrounds to OWE while it is running, and the lock keeps its own playback'
+  backgroundQml.includes('videoEnabled: false') &&
+    /property bool videoEnabled: true/.test(mediaQml) &&
+    /active: root\.path !== "" && root\.video && !root\.reloading && root\.videoEnabled/.test(mediaQml) &&
+    !lockQml.includes('videoEnabled'),
+  'the desktop hands video backgrounds to OWE, and the lock keeps its own playback'
+)
+assert(
+  !backgroundQml.includes('playbackEnabled') &&
+    !backgroundQml.includes('sessionObscured') &&
+    !backgroundQml.includes('fullscreenHere') &&
+    !backgroundQml.includes('Hyprland.monitorFor') &&
+    !backgroundQml.includes('omarchy.lock') &&
+    !backgroundQml.includes('omarchy.battery'),
+  'the desktop no longer carries the shell video pause policy'
 )
 assert(
   lockQml.includes('source: wallpaper.video ? null : wallpaper') &&
@@ -102,20 +105,6 @@ assert(
     lockQml.includes('visible: wallpaper.video'),
   'lock screen bypasses its image effect for video output'
 )
-assert(
-  /sessionObscured:\s*lockActive \|\| screensaverActive/.test(backgroundQml) &&
-    backgroundQml.includes('playbackEnabled: !root.sessionObscured && !root.powerSaverActive && !panel.fullscreenHere') &&
-    backgroundQml.includes('omarchy.lock') &&
-    backgroundQml.includes('omarchy.idle') &&
-    backgroundQml.includes('omarchy.battery'),
-  'desktop playback stops while covered or on battery power-saver'
-)
-assert(
-  backgroundQml.includes('Hyprland.monitorFor(modelData)') &&
-    /fullscreenHere: visibleWorkspace \? visibleWorkspace\.hasFullscreen : false/.test(backgroundQml) &&
-    !backgroundQml.includes('ToplevelManager.activeToplevel'),
-  'a fullscreen window pauses only the output it covers, wherever focus is'
-)
 assert(
   /if \(displayedBackground === finalPath\) displayedReloads \+= 1/.test(backgroundQml) &&
     backgroundQml.includes('reloads: root.displayedReloads') &&