Stage 7: regression tests for the polished UI (logic + behaviour)

Lock the polish branch's behaviour so a future UI edit surfaces as a failing
assertion to re-agree or fix.

Unit (vitest, node env):
- placement: recallIndex, cellOccupied/isBlankSlot, non-linear direction, the
  single-tile submit default, and placementFromHint blank-fallback / rack-exhausted.
- banner: the marquee scroll-cycle repeat-then-advance, stop(), root-relative and
  multiple links.
- client.GatewayError. Extract the check-word constraints out of Game.svelte into a
  pure lib/checkword.ts (sanitize + canCheck) and cover them.

E2E (playwright mock, Chromium + WebKit):
- commit via the 🏁 control, history slide-down + close, the exchange dialog,
  check-word input sanitising + verdict, resign-to-finished, and the Settings
  board-label mode changing the on-board labels.

ui/src/lib/checkword.ts

@@ -0,0 +1,31 @@
+// Pure helpers for the in-game "check a word" panel: input sanitising and the gate on
+// when a check may be sent. Kept separate from Game.svelte so the constraints (the
+// variant alphabet, the length bounds, the answered-word cache and the cool-down
+// throttle) are unit-testable and stay in lockstep with the UI.
+
+/** The longest word that fits on a standard 15-cell board line. */
+export const MAX_WORD_LEN = 15;
+/** The shortest word worth checking. */
+export const MIN_WORD_LEN = 2;
+
+/**
+ * sanitizeCheckWord upper-cases the raw input and keeps only characters of the active
+ * variant's alphabet, capped at MAX_WORD_LEN — so the field can never hold something the
+ * dictionary could not contain.
+ */
+export function sanitizeCheckWord(raw: string, alphabet: string[]): string {
+  const allowed = new Set(alphabet);
+  return Array.from(raw.toUpperCase())
+    .filter((ch) => allowed.has(ch))
+    .slice(0, MAX_WORD_LEN)
+    .join('');
+}
+
+/**
+ * canCheckWord gates the Check action: the trimmed word must be of valid length, must not
+ * have been answered already (cached), and must not fall inside the cool-down window.
+ */
+export function canCheckWord(word: string, alreadyChecked: boolean, cooling: boolean): boolean {
+  const w = word.trim();
+  return w.length >= MIN_WORD_LEN && w.length <= MAX_WORD_LEN && !alreadyChecked && !cooling;
+}