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/chat.sql.go

@@ -0,0 +1,71 @@
+// Code generated by sqlc. DO NOT EDIT.
+// versions:
+//   sqlc v1.30.0
+// source: chat.sql
+
+package gen
+
+import (
+	"context"
+)
+
+const createChatMessage = `-- name: CreateChatMessage :exec
+INSERT INTO chat_messages (game_id, nickname, color, message, created_at)
+VALUES (?, ?, ?, ?, ?)
+`
+
+type CreateChatMessageParams struct {
+	GameID    string
+	Nickname  string
+	Color     int64
+	Message   string
+	CreatedAt int64
+}
+
+func (q *Queries) CreateChatMessage(ctx context.Context, arg CreateChatMessageParams) error {
+	_, err := q.db.ExecContext(ctx, createChatMessage,
+		arg.GameID,
+		arg.Nickname,
+		arg.Color,
+		arg.Message,
+		arg.CreatedAt,
+	)
+	return err
+}
+
+const getChatMessages = `-- name: GetChatMessages :many
+SELECT id, game_id, nickname, color, message, created_at FROM chat_messages
+WHERE game_id = ?
+ORDER BY created_at DESC, id DESC
+LIMIT 50
+`
+
+func (q *Queries) GetChatMessages(ctx context.Context, gameID string) ([]ChatMessage, error) {
+	rows, err := q.db.QueryContext(ctx, getChatMessages, gameID)
+	if err != nil {
+		return nil, err
+	}
+	defer rows.Close()
+	var items []ChatMessage
+	for rows.Next() {
+		var i ChatMessage
+		if err := rows.Scan(
+			&i.ID,
+			&i.GameID,
+			&i.Nickname,
+			&i.Color,
+			&i.Message,
+			&i.CreatedAt,
+		); err != nil {
+			return nil, err
+		}
+		items = append(items, i)
+	}
+	if err := rows.Close(); err != nil {
+		return nil, err
+	}
+	if err := rows.Err(); err != nil {
+		return nil, err
+	}
+	return items, nil
+}