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>

.changes/playback-live-player-switch.md

@@ -0,0 +1,10 @@
+---
+type: fix
+area: playback
+---
+
+Switching the video player — from the command palette or the settings page —
+now takes effect immediately on an already-playing Xtream or Stalker stream
+instead of waiting for the player to be reopened. Playback also starts with
+the saved player right away, without briefly mounting the default engine
+first.