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>

scala/solutions/Runtime.scala

@@ -5,9 +5,12 @@ trait Platform:
   def fillRect(x: Int, y: Int, w: Int, h: Int, color: String): Unit
   def fillText(x: Int, y: Int, text: String, color: String, size: Int, align: String): Unit
   def randomSeed(): Long
+  def loadBest(): Int               // m10
+  def saveBest(score: Int): Unit    // m10
   def startClock(onTime: Long => Unit): Unit
   def onKeyDown(cb: String => Unit): Unit
   def onKeyUp(cb: String => Unit): Unit
+  def onClick(cb: (Int, Int) => Unit): Unit // m13
 
 /**
  * m09 runtime: the single impure place in the course (with the web/ glue); everything else only builds values.
@@ -18,6 +21,10 @@ object Runtime:
   // Perform one op on the platform and return its answer.
   private def perform(op: Op, p: Platform): OpResult = op match
     case Op.RandomSeed => OpResult.Seed(p.randomSeed())
+    case Op.LoadBest   => OpResult.Best(p.loadBest())
+    case Op.SaveBest(score) =>
+      p.saveBest(score)
+      OpResult.Done
     case Op.Draw(Shape.Rect(x, y, w, h, color)) =>
       p.fillRect(x, y, w, h, color)
       OpResult.Done
@@ -39,4 +46,6 @@ object Runtime:
       ios.foreach(runIO(_, p))
     p.onKeyDown(key => feed(Event.KeyDown(key)))
     p.onKeyUp(key => feed(Event.KeyUp(key)))
+    // m13: a fourth kind of input. Programs that do not listen for clicks simply ignore them.
+    p.onClick((x, y) => feed(Event.Click(x, y)))
     p.startClock(t => feed(Event.Time(t)))