feat: add FastAPI app factory and health check endpoint

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

tests/test_config.py

@@ -11,10 +11,14 @@ class TestSettings:
 
     def test_settings_loads_defaults(self) -> None:
         """Settings should have sensible defaults for all fields."""
-        with patch.dict(os.environ, {
+        env = {
             "ADMIN_USERNAME": "testadmin",
             "ADMIN_PASSWORD": "testpass123",
-        }, clear=False):
+        }
+        # Remove DATABASE_URL so we test the actual default
+        env_clean = {k: v for k, v in os.environ.items() if k != "DATABASE_URL"}
+        env_clean.update(env)
+        with patch.dict(os.environ, env_clean, clear=True):
             settings = Settings()
             assert settings.admin_username == "testadmin"
             assert settings.admin_password == "testpass123"