fix(player): re-arm the cursor idle timer when playback changes

The idle countdown that hides the cursor and the play/pause overlay was only
started from mousemove. A cursor that stayed still over the player while a
click, a key or a scrub release started playback never got a countdown, so
the overlay stayed on the video until the mouse moved again.

Arm the timer from one place and rerun it whenever playback or fullscreen
changes, keeping the cursor-over-player state in a ref so the same rule
applies from every entry point.

components/video-page-content.tsx

@@ -214,7 +214,6 @@ export function VideoPageContent({
     setActiveVersionId,
   });
 
-  // Cursor idle detection: hide overlay when cursor idle for 3s while playing
   // Memoize version selection handler to prevent recreating on each render
   const handleVersionSelect = useCallback(
     (versionId: string) => {

components/video-page/hooks/use-video-player.ts

@@ -34,6 +34,9 @@ import {
   timeFromClientX as timeFromClientXWithin,
 } from '@/components/video-page/hooks/video-player-utils';
 
+/** How long the cursor has to sit still over the player before it and the overlay hide. */
+const CURSOR_IDLE_DELAY_MS = 1000;
+
 interface UseVideoPlayerParams {
   activeVersion: Version | undefined;
   activeVersionId: string | null;
@@ -116,6 +119,7 @@ export function useVideoPlayer({
   const [bunnyPortraitFrameWidth, setBunnyPortraitFrameWidth] = useState<number>(0);
   const [cursorIdle, setCursorIdle] = useState(false);
   const cursorIdleTimerRef = useRef<ReturnType<typeof setTimeout> | null>(null);
+  const isCursorOverPlayerRef = useRef(false);
   const bunnyRetryTimerRef = useRef<ReturnType<typeof setTimeout> | null>(null);
   const bunnyFrameCallbackIdRef = useRef<number | null>(null);
   const bunnyFrameSampleRef = useRef<{ mediaTime: number; presentedFrames: number } | null>(null);
@@ -212,29 +216,41 @@ export function useVideoPlayer({
     return () => observer.disconnect();
   }, [activeVersionId, bunnyViewportRef]);
 
-  const handleVideoMouseMove = useCallback(() => {
-    setCursorIdle(false);
+  // Restart the idle countdown from "cursor active". The cursor only counts as
+  // idle while it is over the player and there is something to hide (playback
+  // running, or fullscreen chrome); otherwise it stays visible.
+  const armCursorIdleTimer = useCallback(() => {
     if (cursorIdleTimerRef.current) clearTimeout(cursorIdleTimerRef.current);
+    cursorIdleTimerRef.current = null;
+    setCursorIdle(false);
 
-    const shouldHideControls = isFullscreenMode;
+    if (!isCursorOverPlayerRef.current) return;
+    if (!isPlaying && !isFullscreenMode) return;
 
-    if (isPlaying || shouldHideControls) {
-      cursorIdleTimerRef.current = setTimeout(() => {
-        setCursorIdle(true);
-      }, 1000);
-    }
+    cursorIdleTimerRef.current = setTimeout(() => {
+      setCursorIdle(true);
+    }, CURSOR_IDLE_DELAY_MS);
   }, [isFullscreenMode, isPlaying]);
 
-  const handleVideoMouseLeave = useCallback(() => {
-    if (cursorIdleTimerRef.current) clearTimeout(cursorIdleTimerRef.current);
-    setCursorIdle(false);
-  }, []);
+  const handleVideoMouseMove = useCallback(() => {
+    isCursorOverPlayerRef.current = true;
+    armCursorIdleTimer();
+  }, [armCursorIdleTimer]);
 
+  const handleVideoMouseLeave = useCallback(() => {
+    isCursorOverPlayerRef.current = false;
+    armCursorIdleTimer();
+  }, [armCursorIdleTimer]);
+
+  // Playback can change without the cursor moving: a click or a key starts it,
+  // and a scrub pauses then resumes it. Each of those needs a fresh countdown,
+  // or a still cursor over the player never goes idle and the overlay stays.
   useEffect(() => {
+    armCursorIdleTimer();
     return () => {
       if (cursorIdleTimerRef.current) clearTimeout(cursorIdleTimerRef.current);
     };
-  }, []);
+  }, [armCursorIdleTimer]);
 
   useEffect(() => {
     if (isApiLoaded) return;