feat: persist chat messages to SQLite (#1)

db/migrations/006_add_chat_messages.sql

@@ -0,0 +1,15 @@
+-- +goose Up
+CREATE TABLE chat_messages (
+    id INTEGER PRIMARY KEY AUTOINCREMENT,
+    game_id TEXT NOT NULL,
+    nickname TEXT NOT NULL,
+    color INTEGER NOT NULL,
+    message TEXT NOT NULL,
+    created_at INTEGER NOT NULL,
+    FOREIGN KEY (game_id) REFERENCES games(id) ON DELETE CASCADE
+);
+CREATE INDEX idx_chat_messages_game ON chat_messages(game_id, created_at);
+
+-- +goose Down
+DROP INDEX IF EXISTS idx_chat_messages_game;
+DROP TABLE IF EXISTS chat_messages;