feat: persist chat messages to SQLite

Chat messages were ephemeral — lost on page refresh or late join.
Add a chat_messages table and load the last 50 messages on connect
so players see conversation history.

main.go

@@ -27,9 +27,10 @@ import (
 )
 
 var (
-	store      = game.NewGameStore()
-	snakeStore = snake.NewSnakeStore()
-	queries    *gen.Queries
+	store         = game.NewGameStore()
+	snakeStore    = snake.NewSnakeStore()
+	queries       *gen.Queries
+	chatPersister *db.ChatPersister
 )
 
 //go:embed assets
@@ -61,6 +62,7 @@ func main() {
 	queries = gen.New(db.DB)
 	store.SetPersister(db.NewGamePersister(queries))
 	snakeStore.SetPersister(db.NewSnakePersister(queries))
+	chatPersister = db.NewChatPersister(queries)
 
 	sessionManager, err := via.NewSQLiteSessionManager(db.DB)
 	if err != nil {
@@ -356,7 +358,7 @@ func main() {
 		colSignal := c.Signal(0)
 		showGuestPrompt := c.Signal(false)
 		chatMsg := c.Signal("")
-		var chatMessages []ui.C4ChatMessage
+		chatMessages, _ := chatPersister.LoadChatMessages(gameID)
 		var chatMu sync.Mutex
 
 		goToLogin := c.Action(func() {
@@ -462,6 +464,7 @@ func main() {
 				Message:  msg,
 				Time:     time.Now().UnixMilli(),
 			}
+			chatPersister.SaveChatMessage(gameID, cm)
 			data, err := json.Marshal(cm)
 			if err != nil {
 				return