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/lib/playerModalHooks.apiload.dom.test.tsx

@@ -30,6 +30,7 @@ function mountPlayer(setPlayerError: (code: number | null) => void) {
     useYtProgress({
       activeId: VID,
       resumeAt: 0,
+      exactStart: false,
       mountRef: { current: mount },
       playerRef: createRef<YTPlayer>() as RefObject<YTPlayer | null>,
       currentIdRef: { current: VID },