feat(course): audit fixes and twelve extensions (Modules 7b, 12, 13)

Audit pass:
- Frame rule counts frames since the last move, so every step lasts
  exactly movesEvery(score) frames, also right after a speed-up
- clampTime + MAX_GAP_MS: a hidden tab no longer replays the whole gap
- Pong Restart keeps held keys
- Fact corrections (mulberry32 output coverage, Haskell IO, uniform)
- New fixture cases from a mutation analysis

Extensions (all three tracks, shared fixtures, course text):
- Turn queue (Exercise 10.6), persisted high score (10.7),
  replay viewer (10.8), play() end-to-end helper (9.5)
- Optional State (4.7) and optional Module 7b, stack-safe IO
- Module 12, property-based testing with generators, shrinking,
  invariants and a model-based oracle
- Module 13, Conway's Life with a Click event
- JS type checking via jsconfig, JSDoc and types.d.ts
- Maintainer tools: scripts/mutate.mjs, scripts/typecheck-js.sh,
  Playwright end-to-end suite (e2e/, scripts/e2e.sh)

Docs: docs/contract.md is the canonical contract; specs and build log
under docs/superpowers.

Verified: JS 728, Scala 689, F# 691 unit tests; stubs and progression
M01-M13 and M07b; 176 end-to-end tests on Chromium and WebKit.

Co-Authored-By: Claude Fable 5.2 <noreply@anthropic.com>

js/solutions/rules.js

@@ -1,24 +1,29 @@
 // m03 rules: the pure game rules. Each function takes a state and returns a new one.
 import { contains, dropLast } from './util.js'
 import { pointEquals, point, delta, opposite } from './model.js'
+/** @import { Point, Direction, GameState } from './types' */
 
-/** The cell one step from `p` in direction `dir`. No wrapping: it may land outside the board. */
+/** The cell one step from `p` in direction `dir`. No wrapping: it may land outside the board.
+ * @type {(p: Point, dir: Direction) => Point} */
 export const move = (p, dir) => {
   const d = delta(dir)
   return point(p.x + d.x, p.y + d.y)
 }
 
-/** True if `p` lies on the board. */
+/** True if `p` lies on the board.
+ * @type {(state: {width: number, height: number}, p: Point) => boolean} */
 export const inBounds = (state, p) => p.x >= 0 && p.x < state.width && p.y >= 0 && p.y < state.height
 
 /**
  * Ask to turn. We compare with `dir` (where the snake last moved), not `nextDir`:
  * otherwise Up-then-Left within one tick would turn a Right-moving snake back onto itself.
+ * @type {(state: GameState, dir: Direction) => GameState}
  */
 export const turn = (state, dir) =>
   state.status === 'Playing' && dir !== opposite(state.dir) ? { ...state, nextDir: dir } : state
 
-/** One step of the game. */
+/** One step of the game.
+ * @type {(state: GameState) => GameState} */
 export const advance = (state) => {
   if (state.status !== 'Playing') return state
   const d = state.nextDir