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.contract.test.ts

@@ -0,0 +1,34 @@
+import { readdirSync, readFileSync } from "node:fs";
+import { describe, expect, it } from "vitest";
+
+// The whole app source: a state write can be made from any page.
+const root = new URL("../../", import.meta.url);
+const sources = () =>
+  readdirSync(root, { recursive: true, encoding: "utf8" })
+    .map((f) => f.replace(/\\/g, "/"))
+    .filter((f) => /\.tsx?$/.test(f) && !f.includes(".test."))
+    .map((f) => ({ f, src: readFileSync(new URL(f, root), "utf8") }));
+
+// The api's own definitions of these writes, and the one module that may call them.
+const ALLOWED = new Set([
+  "lib/api/feed.ts",
+  "lib/api/playlists.ts",
+  "features/video/videoWrites.ts",
+]);
+
+// A related list and a live search are never refetched, so a state or Watch-later write that does
+// not reach them (`markVideo`) leaves them showing the old mark for the session. videoWrites makes
+// those writes and the mark together; a direct api call skips the mark.
+describe("a video's state and Watch-later writes", () => {
+  it("go through features/video/videoWrites, never the api directly", () => {
+    const offenders = sources()
+      .filter(({ f }) => !ALLOWED.has(f))
+      // Only a call on the api object counts (React's own `setState` is not ours); the dot may sit
+      // on the next line of a chain.
+      .filter(({ src }) =>
+        /\bapi\s*\.\s*(setState|clearState|watchLaterAdd|watchLaterRemove)\(/.test(src),
+      )
+      .map(({ f }) => f);
+    expect(offenders).toEqual([]);
+  });
+});