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/gen/models.go

@@ -0,0 +1,37 @@
+// Code generated by sqlc. DO NOT EDIT.
+// versions:
+//   sqlc v1.30.0
+
+package gen
+
+import (
+	"database/sql"
+)
+
+type Game struct {
+	ID           string
+	Board        string
+	CurrentTurn  int64
+	Status       int64
+	WinnerUserID sql.NullString
+	WinningCells sql.NullString
+	CreatedAt    sql.NullTime
+	UpdatedAt    sql.NullTime
+}
+
+type GamePlayer struct {
+	GameID        string
+	UserID        sql.NullString
+	GuestPlayerID sql.NullString
+	Nickname      string
+	Color         int64
+	Slot          int64
+	CreatedAt     sql.NullTime
+}
+
+type User struct {
+	ID           string
+	Username     string
+	PasswordHash string
+	CreatedAt    sql.NullTime
+}