fix(client): add anti-echo guard for video syncing (#166)

Added an anti-echo guard to prevent play/pause event spams.

<!-- CURSOR_SUMMARY -->
---

> [!NOTE]
> **Medium Risk**
> Touches client-side video play/pause state synchronization; a small
logic change could still cause playback state to get stuck or miss
updates on some browsers (notably Safari).
> 
> **Overview**
> Prevents play/pause “echo” loops between the Vuex `playing` watcher
and the `<video>` element by introducing an `isVideoSyncing` guard.
> 
> When native `playing`/`pause` events fire, the component temporarily
marks itself as syncing and defers clearing the flag to the next tick,
avoiding Safari timing races where events can precede `video.paused`
updates.
> 
> <sup>Written by [Cursor
Bugbot](https://cursor.com/dashboard?tab=bugbot) for commit
ee912e3. This will update automatically
on new commits. Configure
[here](https://cursor.com/dashboard?tab=bugbot).</sup>
<!-- /CURSOR_SUMMARY -->

Co-authored-by: Rafael <raf@kernel.sh>

Author: AbdulRashidReshamwala

images/chromium-headful/client/src/components/video.vue

@@ -260,6 +260,7 @@
     private focused = false
     private fullscreen = false
     private mutedOverlay = true
+    private isVideoSyncing = false
 
     get admin() {
       return this.$accessor.user.admin
@@ -431,6 +432,10 @@
 
     @Watch('playing')
     async onPlayingChanged(playing: boolean) {
+      // In Safari, native events can fire slightly before the `video.paused` property flips.
+      // This anti-echo guard prevents the watcher from fighting the video element's own state changes.
+      if (this.isVideoSyncing) return;
+
       if (this._video && this._video.paused && playing) {
         // if autoplay is disabled, play() will throw an error
         // and we need to properly save the state otherwise we
@@ -511,11 +516,15 @@
       })
 
       this._video.addEventListener('playing', () => {
+        this.isVideoSyncing = true
         this.$accessor.video.play()
+        this.$nextTick(() => { this.isVideoSyncing = false })
       })
 
       this._video.addEventListener('pause', () => {
+        this.isVideoSyncing = true
         this.$accessor.video.pause()
+        this.$nextTick(() => { this.isVideoSyncing = false })
       })
 
       /* Initialize Guacamole Keyboard */