feat(players): keep a video playing in the background on Brave iOS; repeat on the watch page

On iPad Brave, a shared video stopped the moment the browser left the
foreground, even with Brave's "Enable Background Audio" on, while an mp3
kept playing. Brave iOS keeps a web <video> going by re-playing one the OS
paused (brave-core ios/browser/web/media/resources/media_backgrounding.ts),
but it only hooks a <video> present at document start or added as a
MutationObserver addedNode that IS a video. React inserts a player's
<video> inside its freshly mounted wrapper in one go, so Brave never saw it.

lib/browserBackgroundPlay re-inserts a mounted <video> at its own position,
once per element: it becomes an added node, the DOM React manages does not
change, and playback is not interrupted. The watch page, the downloads
library player and the Plex player hand their <video> to it. Measured on the
owner's iPad (Brave) with a prototype of the same idea: the video kept
playing in another app and with the screen locked. The YouTube modal is not
ours to change: its <video> lives in YouTube's cross-origin iframe, and
nothing of ours pauses it on backgrounding.

The prototype's two audio-element variants (a muted video following an
<audio>, and an <audio> taking over on hide) went silent in the background on
the iPad and are removed.

The watch page gets a Repeat toggle, on by default and remembered per
browser (LS.watchRepeat; the page has no account): it sets `loop` on the
<video> or the audio-only <audio>.

frontend/src/lib/storage.ts

@@ -65,6 +65,9 @@ export const LS = {
   notifSettings: "siftlode.notifSettings",
   onboardingDismissed: "siftlode.onboarding.dismissed",
   seenVersion: "siftlode.seenVersion",
+  // The public /watch page's repeat toggle ("0" = off; on by default). Browser-wide, NOT per account:
+  // that page runs outside the app, with no account at all.
+  watchRepeat: "siftlode.watchRepeat",
   chatDock: (userId: number) => `siftlode.chatDock.${userId}`,
 } as const;