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/modules/channels/WatchedVideosDialog.tsx

@@ -3,7 +3,7 @@ import { useTranslation } from "react-i18next";
 import { useQuery, useQueryClient } from "@tanstack/react-query";
 import { EyeOff, Play, UserPlus } from "lucide-react";
 import { qk } from "../../lib/queryKeys";
-import { patchRelated } from "../../lib/progressCache";
+import { writeVideoState } from "../../features/video/videoWrites";
 import { api, type Video, type VideoStatus, type WatchedChannel } from "../../lib/api";
 import { formatDate, formatDuration } from "../../lib/format";
 import { notifyActionError } from "../../lib/actionErrors";
@@ -54,8 +54,7 @@ export default function WatchedVideosDialog({
 
   // The player's watched / in-progress marks: saved, then shown on this list and the feed's.
   const onState = useStableCallback((id: string, status: VideoStatus) => {
-    api
-      .setState(id, status)
+    writeVideoState(qc, id, status)
       .then(() => {
         qc.setQueryData(
           key,
@@ -66,8 +65,6 @@ export default function WatchedVideosDialog({
             },
         );
         void qc.invalidateQueries({ queryKey: qk.feed() });
-        // The player's related lists are never refetched: the mark goes into them.
-        patchRelated(qc, id, { status });
       })
       .catch((e: unknown) => notifyActionError(e, t("errors.writeFailed.videoState")));
   });