chore(backend): add shared theme id catalog for matchmaking/rooms

backend/src/themeIds.js

@@ -0,0 +1,28 @@
+// Backend-side copy of the frontend's theme id catalog
+// (frontend/src/data/themes.ts's `THEMES` object keys), kept in sync by hand
+// per backend/src/PROTOCOL.md's snippet/theme identity contracts — the
+// backend never needs theme *content* (hex palettes), only valid ids, to:
+//   - pick a random theme for matchmaking matches and `themeMode: 'random'`
+//     private-room matches (excluding the previous match's theme, see
+//     backend/src/rooms/room.js), and
+//   - offer the full theme set as `vote:start`'s `themeIds` for
+//     `themeMode: 'chosen'` private rooms (see backend/src/rooms/themeVote.js).
+//
+// If frontend/src/data/themes.ts's THEMES keys ever change, update this
+// array to match.
+export const THEME_IDS = [
+  'gruvbox',
+  'tokyoNight',
+  'vscode',
+  'github',
+  'dracula',
+  'catppuccin',
+];
+
+/** Picks a theme id uniformly at random, optionally excluding one id
+ * (used by private rooms to avoid repeating the previous match's theme). */
+export function pickRandomThemeId(excludeId) {
+  const pool = excludeId ? THEME_IDS.filter((id) => id !== excludeId) : THEME_IDS;
+  const candidates = pool.length > 0 ? pool : THEME_IDS;
+  return candidates[Math.floor(Math.random() * candidates.length)];
+}