fix(playback): apply saved player changes to mounted web players

WebPlayerViewComponent resolved the saved engine from a one-shot
StorageMap snapshot taken at mount, so a player switch from the command
palette or settings page confirmed via snackbar and persisted the
setting while an already-mounted Xtream/Stalker player silently kept
the previous engine. The same snapshot also made first play mount the
default Video.js engine and swap to the saved one once the async read
landed.

Resolve the player (and recording folder) from the live SettingsStore
signal instead and drop the snapshot entirely. Precedence is unchanged:
temporary recovery override -> host playerOverride -> saved player ->
Video.js. Hosts passing no override (Xtream/Stalker live layouts, the
portal inline detail player) now track saved changes in place; first
mount reads the already-loaded store, so the default engine no longer
flashes.

Regression coverage (all verified to fail with the fix reverted):
three unit tests on the component and two Xtream live-route e2e tests —
a palette switch reaching the mounted player without a layout remount,
and a MutationObserver engines-ever-seen assertion that the saved
engine mounts first time.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

docs/architecture/embedded-inline-playback.md

@@ -364,7 +364,20 @@ Current contract:
 
 The shared `WebPlayerViewComponent` is the central browser-player viewport for
 M3U, Xtream, and Stalker inline playback, including live streams opened from
-favorites and recently viewed collections. Video.js, HTML5, and ArtPlayer
+favorites and recently viewed collections.
+
+The mounted engine resolves in a fixed order: temporary recovery override →
+host `playerOverride` input → the saved player read from the live
+`SettingsStore` signal (Video.js as the last-resort default). The saved player
+is deliberately NOT a mount-time storage snapshot: persisting a different
+player — from the settings page or the command palette — re-applies to every
+mounted `WebPlayerViewComponent` in place as a new playback application, and a
+first mount reads the already-loaded store value so the default engine never
+flashes before the saved one. Hosts that pass no `playerOverride` (the Xtream
+and Stalker live layouts, the portal inline detail player) rely on this live
+tracking.
+
+Video.js, HTML5, and ArtPlayer
 report native media errors, hls.js errors, Video.js/VHS errors, Shaka errors,
 mpegts.js errors, and HLS manifest codec metadata into the DOM-free classifiers
 exported by `@iptvnator/playback/util`.