fix: avoid NameError in check_external_config_db when the DB is unreachable

docs/en_US/release_notes_9_16.rst

@@ -40,3 +40,4 @@ Bug fixes
   | `Issue #9939 <https://github.com/pgadmin-org/pgadmin4/issues/9939>`_ -  Fix saving a newly-added row in the Query Tool failing when the result set includes expression or alias columns that are not real columns of the underlying table.
   | `Issue #9976 <https://github.com/pgadmin-org/pgadmin4/issues/9976>`_ -  Fix a startup migration crash (NoSuchTableError) when an old configuration database contains a stale foreign-key reference.
   | `Issue #9984 <https://github.com/pgadmin-org/pgadmin4/issues/9984>`_ -  Fix the Docker entrypoint mishandling a quoted PGADMIN_CONFIG_CONFIG_DATABASE_URI, which caused a SQLAlchemy parse error and silently skipped PGADMIN_DEFAULT_EMAIL/PASSWORD setup.
+  | `Issue #10052 <https://github.com/pgadmin-org/pgadmin4/issues/10052>`_ -  Fix a crash when checking an unreachable external configuration database, so first-launch setup proceeds instead of erroring.

web/pgadmin/utils/check_external_config_db.py

@@ -17,11 +17,13 @@ def check_external_config_db(database_uri):
     """
     engine = create_engine(database_uri)
     try:
-        connection = engine.connect()
-        if inspect(engine).has_table("server"):
-            return True
-        return False
+        # The context manager closes the connection on every path. The
+        # previous "finally: connection.close()" raised NameError when
+        # engine.connect() itself failed (e.g. an unreachable database),
+        # masking the intended "return False".
+        with engine.connect():
+            return inspect(engine).has_table("server")
     except Exception:
         return False
     finally:
-        connection.close()
+        engine.dispose()