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/playlists/Playlists.tsx

@@ -3,7 +3,7 @@ import { useLatest, useStableCallback } from "../../lib/useLatest";
 import { useTranslation } from "react-i18next";
 import { useQuery, useQueryClient } from "@tanstack/react-query";
 import { qk } from "../../lib/queryKeys";
-import { patchRelated } from "../../lib/progressCache";
+import { writeVideoState } from "../../features/video/videoWrites";
 import {
   DndContext,
   KeyboardSensor,
@@ -611,16 +611,13 @@ function PlaylistDetail() {
   }
 
   function playerState(id: string, status: VideoStatus) {
-    api
-      .setState(id, status)
+    writeVideoState(qc, id, status)
       .then(() => {
         // Every cached list, not `qk.playlist(selectedId)`: the player may have been launched from a
         // list that is no longer the selected one (see `playing`), and that list holds the row whose
         // status just changed. Only lists actually on screen refetch.
         qc.invalidateQueries({ queryKey: qk.playlist() });
         qc.invalidateQueries({ queryKey: qk.feed() });
-        // The player's related lists are never refetched: the mark goes into them.
-        patchRelated(qc, id, { status });
       })
       // No catch used to mean an unhandled rejection and nothing said.
       .catch((e: unknown) => notifyActionError(e, t("errors.writeFailed.videoState")));