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.

db/gen/models.go

@@ -8,6 +8,15 @@ import (
 	"database/sql"
 )
 
+type ChatMessage struct {
+	ID        int64
+	GameID    string
+	Nickname  string
+	Color     int64
+	Message   string
+	CreatedAt int64
+}
+
 type Game struct {
 	ID            string
 	Board         string