Add user authentication and game persistence with SQLite

- User registration/login with bcrypt password hashing
- SQLite database with goose migrations and sqlc-generated queries
- Games and players persisted to database, resumable after restart
- Guest play still supported alongside authenticated users
- Auth UI components (login/register forms, auth header, guest banner)

db/db.go

@@ -0,0 +1,33 @@
+package db
+
+import (
+	"database/sql"
+	"embed"
+
+	"github.com/pressly/goose/v3"
+	_ "modernc.org/sqlite"
+)
+
+//go:embed migrations/*.sql
+var migrations embed.FS
+
+var DB *sql.DB
+
+func Init(dbPath string) error {
+	var err error
+	DB, err = sql.Open("sqlite", dbPath+"?_journal_mode=WAL&_busy_timeout=5000")
+	if err != nil {
+		return err
+	}
+	DB.SetMaxOpenConns(1)
+
+	goose.SetBaseFS(migrations)
+	if err := goose.SetDialect("sqlite3"); err != nil {
+		return err
+	}
+	if err := goose.Up(DB, "migrations"); err != nil {
+		return err
+	}
+
+	return nil
+}