Stage 17 round 6 (#11/#12): quick-game variant plaques with rules, flag, and move-limit

Each auto-match variant is now a lobby-style plaque: the display name with a flag on the
right (🇺🇸 / 🇷🇺; Erudit uses a bundled minimalist USSR flag SVG) and a one-line rules
summary below — bag size, the ё rule, and bonus differences, sourced from the engine
rulesets (Scrabble 100 · Скрэббл 104, ё a letter · Эрудит 131, ё=е, no centre ×2, +15).
The move-time limit (24h auto-match clock) is shown under the buttons. e2e locks it.

(Multiple-words-per-move is the same for every variant, so it is described in About/landing
rather than repeated on each button.)

ui/src/lib/variants.ts

@@ -28,6 +28,22 @@ export function variantNameKey(v: Variant): MessageKey {
   return ALL_VARIANTS.find((o) => o.id === v)?.label ?? 'new.english';
 }
 
+// VARIANT_RULES is the i18n key for each variant's one-line rules summary on the New Game
+// buttons (bag size, the ё rule, bonus differences), sourced from the engine rulesets.
+export const VARIANT_RULES: Record<Variant, MessageKey> = {
+  english: 'new.rulesEnglish',
+  russian_scrabble: 'new.rulesRussian',
+  erudit: 'new.rulesErudit',
+};
+
+// VARIANT_FLAG is the flag shown on a variant button: an emoji for the Scrabble variants;
+// Erudit uses the bundled USSR flag SVG (public/flag-ussr.svg), so its entry is empty.
+export const VARIANT_FLAG: Record<Variant, string> = {
+  english: '🇺🇸',
+  russian_scrabble: '🇷🇺',
+  erudit: '',
+};
+
 // VARIANT_LANGUAGE maps each variant to its game language. en -> English;
 // ru -> Russian + Эрудит.
 export const VARIANT_LANGUAGE: Record<Variant, 'en' | 'ru'> = { english: 'en', russian_scrabble: 'ru', erudit: 'ru' };