Pills only with the controls, web links in their final layout at once, chat pop-ups when paused by default

- Next episode (known ending, else the last two minutes) and Skip ED
  show only while the controls are up, like Skip 1:30 (PillGate).
- A web link's name and wide cover slot show from the first state, so
  nothing flips when its thumbnail arrives.
- Chat pop-ups default to Only when paused.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

apps/desktop/test/jellyfin_e2e_test.dart

@@ -301,9 +301,9 @@ void main() {
         a.toggleReady();
         await _poll(() => all.every((x) => x.playback.player.state.playing), 'playing again');
 
-        // No known ending (no Outro segment, no ED chapter): no floating
-        // "Next episode" prompt mid-episode, only the card at the end.
-        expect(a.nextPromptVisible.peek(), isFalse);
+        // Account holders see the "Next episode" prompt (this item is
+        // shorter than its 2 min lead); the guest cannot put it up.
+        await _poll(() => a.nextPromptVisible.peek(), 'next prompt');
         expect(b.nextPromptVisible.peek(), isFalse);
 
         // Alice and the guest pick English; it carries to the next episode.