fix(db): add 'math-sprint' to database schema enums

Update all database schemas to include 'math-sprint':
- arcade-rooms.ts: Add to gameName enum
- arcade-sessions.ts: Add to currentGame enum
- room-game-configs.ts: Add to gameName enum and documentation

CRITICAL ISSUE DEMONSTRATED:
This is the schema coupling problem (Issue #1 from AUDIT_2).
Must manually update database schemas for every new game.
Breaks modularity - cannot "just register and go".

Without this change, TypeScript compilation fails with:
  Type '"math-sprint"' is not assignable to type '...'

Recommendation from audit: Change schemas to accept any string,
validate against registry at runtime instead of compile-time enums.

apps/web/src/db/schema/arcade-rooms.ts

@@ -34,7 +34,7 @@ export const arcadeRooms = sqliteTable('arcade_rooms', {
 
   // Game configuration (nullable to support game selection in room)
   gameName: text('game_name', {
-    enum: ['matching', 'memory-quiz', 'complement-race', 'number-guesser'],
+    enum: ['matching', 'memory-quiz', 'complement-race', 'number-guesser', 'math-sprint'],
   }),
   gameConfig: text('game_config', { mode: 'json' }), // Game-specific settings (nullable when no game selected)
 

apps/web/src/db/schema/arcade-sessions.ts

@@ -17,7 +17,7 @@ export const arcadeSessions = sqliteTable('arcade_sessions', {
 
   // Session metadata
   currentGame: text('current_game', {
-    enum: ['matching', 'memory-quiz', 'complement-race', 'number-guesser'],
+    enum: ['matching', 'memory-quiz', 'complement-race', 'number-guesser', 'math-sprint'],
   }).notNull(),
 
   gameUrl: text('game_url').notNull(), // e.g., '/arcade/matching'

apps/web/src/db/schema/room-game-configs.ts

@@ -20,7 +20,7 @@ export const roomGameConfigs = sqliteTable(
 
     // Game identifier
     gameName: text('game_name', {
-      enum: ['matching', 'memory-quiz', 'complement-race', 'number-guesser'],
+      enum: ['matching', 'memory-quiz', 'complement-race', 'number-guesser', 'math-sprint'],
     }).notNull(),
 
     // Game-specific configuration JSON
@@ -28,6 +28,8 @@ export const roomGameConfigs = sqliteTable(
     // - matching: { gameType, difficulty, turnTimer }
     // - memory-quiz: { selectedCount, displayTime, selectedDifficulty, playMode }
     // - complement-race: TBD
+    // - number-guesser: { minNumber, maxNumber, roundsToWin }
+    // - math-sprint: { difficulty, questionsPerRound, timePerQuestion }
     config: text('config', { mode: 'json' }).notNull(),
 
     // Timestamps