fix: address code review issues from final review

- Override modes now actually affect component visibility (force_show,
  force_hide, auto respected in transitions and updates)
- RoomCodeDisplay.update() guarded by #active flag to prevent
  re-activation outside lobby state
- broadcastUpdate() only sends to components when in lobby state
- Relaxed idle→playing/ended transitions for out-of-order events
- room.disconnected now clears room code, players, lobby state context
- Empty room codes clear input fields instead of leaving stale values
- Removed dead auto-mode-toggle UI and associated CSS
- Fixed player list vertical centering when offset is applied

Made-with: Cursor

js/player-list.js

@@ -215,7 +215,7 @@ export class PlayerList {
     const emptyColor = inputs.emptyColor.value;
     const offsetY = `${parseInt(inputs.offset.value, 10) || 0}px`;
 
-    container.style.transform = `translateY(${offsetY})`;
+    container.style.transform = `translateY(calc(-50% + ${offsetY}))`;
 
     for (const slot of this._slots) {
       slot.nameEl.style.fontSize = fontPx;