Suspend rotation while a live wallpaper is on screen

The extension's own log showed rotation kept firing ("Wallpaper
changed to ...") after live wallpaper playback had already started.
Each rotation change writes org.gnome.desktop.background's
picture-uri, which makes GNOME Shell repaint its own background actor
into the same _backgroundGroup our live wallpaper actor lives in,
landing on top of it and hiding the video/GIF entirely.

LiveWallpaperManager now takes an onActiveChanged callback, invoked
only on actual start/stop transitions, which extension.js uses to
suspend/unsuspend RotationManager. This is tracked separately from
user-initiated pause()/resume() so turning live wallpaper off restores
whatever rotation state the user actually had, and next()/previous()
now no-op while suspended so manual/forced-OLED wallpaper changes
can't sneak one in either. The indicator's "Next Wallpaper" item is
greyed out to match.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_019RDqbdjsiisSU7CbQke4g8

lib/rotationManager.js

@@ -31,6 +31,7 @@ export class RotationManager {
         this._timeoutId = 0;
         this._settingsSignals = [];
         this._paused = false;
+        this._suspended = false;
         this._lastChangeTime = GLib.get_monotonic_time();
         this._currentPath = null;
         this._transitionOverlays = [];
@@ -89,7 +90,7 @@ export class RotationManager {
     _restartTimer() {
         this._clearTimer();
 
-        if (this._paused || !this._settings.get_boolean(SettingsKey.ROTATION_ENABLED))
+        if (this._paused || this._suspended || !this._settings.get_boolean(SettingsKey.ROTATION_ENABLED))
             return;
 
         const interval = Math.max(
@@ -118,7 +119,30 @@ export class RotationManager {
         this._restartTimer();
     }
 
+    /**
+     * Distinct from user-initiated pause(): called while a live wallpaper
+     * is actually covering the desktop, so rotation doesn't keep changing
+     * a static image nobody can see (which also churns the shell's own
+     * background actor on top of the live wallpaper's). Resuming restores
+     * whatever the user's own pause() state was, rather than forcing
+     * rotation back on.
+     */
+    suspend() {
+        this._suspended = true;
+        this._clearTimer();
+    }
+
+    unsuspend() {
+        this._suspended = false;
+        this._restartTimer();
+    }
+
     async next({forced = false} = {}) {
+        if (this._suspended) {
+            this._logger.debug('Rotation suspended while live wallpaper is active');
+            return;
+        }
+
         if (this._images.length === 0)
             await this._reloadImages();
 
@@ -144,7 +168,7 @@ export class RotationManager {
     }
 
     async previous() {
-        if (this._images.length === 0)
+        if (this._suspended || this._images.length === 0)
             return;
 
         const mode = this._settings.get_string(SettingsKey.ROTATION_MODE);