fix(lab): make replay pause authoritative

apps/control-station/src/components/laboratory/useRecordedEvidencePlayback.ts

@@ -40,6 +40,23 @@ export function advanceRecordedEvidencePlayback(
   return { ...playback, currentSeconds: clampRecordedEvidenceSeconds(next, range) };
 }
 
+export function synchronizeRecordedEvidencePlayback(
+  current: RecordedObservationPlayback,
+  observed: RecordedObservationPlayback,
+  range: RecordedEvidencePlaybackRange,
+): RecordedObservationPlayback {
+  const currentSeconds = clampRecordedEvidenceSeconds(observed.currentSeconds, range);
+  return {
+    ...current,
+    currentSeconds,
+    // The transport button owns play/pause intent. A native frame callback may
+    // still report the previous media state immediately after an operator
+    // command, so it must not restart playback. The sealed end is the only
+    // media-clock transition allowed to stop the shared LAB clock.
+    playing: currentSeconds >= range.endSeconds ? false : current.playing,
+  };
+}
+
 export function useRecordedEvidencePlayback(
   range: RecordedEvidencePlaybackRange | null,
   { clock = "animation" }: { clock?: "animation" | "external" } = {},
@@ -106,11 +123,7 @@ export function useRecordedEvidencePlayback(
 
   const synchronize = useCallback((next: RecordedObservationPlayback) => {
     if (!validRange(range) || !Number.isFinite(next.currentSeconds)) return;
-    setPlayback((current) => ({
-      ...current,
-      currentSeconds: clampRecordedEvidenceSeconds(next.currentSeconds, range),
-      playing: next.playing,
-    }));
+    setPlayback((current) => synchronizeRecordedEvidencePlayback(current, next, range));
   }, [range]);
 
   return useMemo(() => ({