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/sqlc.yaml

@@ -0,0 +1,9 @@
+version: "2"
+sql:
+  - engine: "sqlite"
+    queries: "queries"
+    schema: "migrations"
+    gen:
+      go:
+        package: "gen"
+        out: "gen"