fix(player): related marks survive, Restart restarts, and refused pages offer nothing to click

- Every state and Watch-later write goes through features/video/videoWrites,
  which marks the never-refetched lists (related lists, live searches) once
  the server has it; a contract test holds it. The Notification Center's
  undo, the feed's reset and the Watch-later toggles skipped it before.
- Confirmed marks are also kept apart (qk.videoMarks) and laid over the
  related rows: a Show more page landing later rebuilt them from the pages
  it read when it started, and dropped a mark made meanwhile.
- Restart on a related video starts at 0 (the session's stored position
  won before), and on the one already playing it seeks.
- The watched toggle remembers each video's mark: Back showed the opened
  video's launch-time state after a related one was marked.
- The help sheet leaves out the player's keys while a layer above it has
  them waiting.
- After a refusal a retry cannot answer, neither Show more (related) nor
  Load more (live search) is offered; a failed live-search page keeps the
  results already read and says why under them.
- The related cap message counts requests, as the cap does.

frontend/src/features/video/videoWrites.ts

@@ -0,0 +1,34 @@
+import type { QueryClient } from "@tanstack/react-query";
+
+import { api, type VideoStatus } from "../../lib/api";
+import { markVideo } from "../../lib/progressCache";
+
+// A video's user state and its Watch-later mark, written to the server and — once it has the
+// change — into the lists that are never refetched (`markVideo`: every related list, every live
+// search). These are the ONE way to make those writes, and `videoWrites.contract.test.ts` holds it:
+// four writes that called the api directly (the Notification Center's undo, the feed's reset, the
+// feed's and Home's Watch-later toggles) left a related list hiding a video the user had un-hidden,
+// or showing it unsaved after a save. Each returns the server's answer, so a caller keeps its own
+// optimistic layer, notices and rollback.
+
+export function writeVideoState(qc: QueryClient, id: string, status: VideoStatus) {
+  return api.setState(id, status).then((r) => {
+    markVideo(qc, id, { status });
+    return r;
+  });
+}
+
+/** Back to pristine: the state row and its resume position both go. */
+export function resetVideoState(qc: QueryClient, id: string) {
+  return api.clearState(id).then((r) => {
+    markVideo(qc, id, { status: "new", position_seconds: 0 });
+    return r;
+  });
+}
+
+export function writeWatchLater(qc: QueryClient, id: string, saved: boolean) {
+  return (saved ? api.watchLaterAdd(id) : api.watchLaterRemove(id)).then((r) => {
+    markVideo(qc, id, { saved });
+    return r;
+  });
+}