diff --git a/web/pgadmin/utils/check_external_config_db.py b/web/pgadmin/utils/check_external_config_db.py
index e7b57d2fb37..320a5c00b88 100644
--- a/web/pgadmin/utils/check_external_config_db.py
+++ b/web/pgadmin/utils/check_external_config_db.py
@@ -16,12 +16,22 @@ def check_external_config_db(database_uri):
     Check if external config database exists if it
     is being used.
     """
-    engine = create_engine(normalize_database_uri(database_uri))
-    connection = None
+    engine = None
     try:
-        connection = engine.connect()
-        return inspect(engine).has_table("server")
+        engine = create_engine(normalize_database_uri(database_uri))
+        with engine.connect():
+            return inspect(engine).has_table("server")
+    except Exception:
+        # Anything that stops us reaching the database, a wrong password or
+        # an unreachable host as much as a malformed URI, is reported as
+        # "there is no external configuration database". The container
+        # entrypoint relies on that so first launch still creates the user
+        # from PGADMIN_DEFAULT_EMAIL and PGADMIN_DEFAULT_PASSWORD (#9984)
+        # rather than leaving an installation nobody can log in to.
         return False
     finally:
-        if connection:
-            connection.close()
+        # Guarded because create_engine() itself rejects a malformed URI, and
+        # an unbound name in the cleanup path is what caused this bug in the
+        # first place.
+        if engine is not None:
+            engine.dispose()
diff --git a/web/pgadmin/utils/tests/test_check_external_config_db.py b/web/pgadmin/utils/tests/test_check_external_config_db.py
new file mode 100644
index 00000000000..9b83bba8f34
--- /dev/null
+++ b/web/pgadmin/utils/tests/test_check_external_config_db.py
@@ -0,0 +1,131 @@
+##########################################################################
+#
+# pgAdmin 4 - PostgreSQL Tools
+#
+# Copyright (C) 2013 - 2026, The pgAdmin Development Team
+# This software is released under the PostgreSQL Licence
+#
+##########################################################################
+
+"""Tests for check_external_config_db().
+
+The container entrypoint calls this to decide whether an external
+configuration database has already been initialised, and treats anything
+other than "True" as "no, so run first-launch setup". It therefore has to
+answer False rather than raise when the database cannot be reached at all,
+which the previous "finally: connection.close()" prevented: engine.connect()
+failing left connection unbound and the NameError escaped in place of the
+answer.
+
+The module is imported the way the entrypoint imports it, as a top level
+module from the directory it lives in, so that this also fails if that
+arrangement is ever broken.
+"""
+
+import os
+import sys
+from urllib.parse import quote
+
+from pgadmin.utils.route import BaseTestGenerator
+from regression.python_test_utils import test_utils as utils
+
+UTILS_DIR = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
+if UTILS_DIR not in sys.path:
+    sys.path.append(UTILS_DIR)
+
+from check_external_config_db import check_external_config_db  # noqa: E402
+
+
+class CheckExternalConfigDBTestCase(BaseTestGenerator):
+    """check_external_config_db() must answer, not raise."""
+
+    scenarios = [
+        ('An unreachable host answers False', dict(
+            case='unreachable')),
+        ('A malformed URI answers False', dict(
+            case='malformed')),
+        ('A reachable database with no server table answers False', dict(
+            case='reachable_without_table')),
+        ('A reachable database with a server table answers True', dict(
+            case='reachable_with_table')),
+    ]
+
+    def setUp(self):
+        self.created_table = False
+        self.db_name = self.server['db']
+
+    def _uri(self):
+        username = quote(str(self.server['username']), safe='')
+        password = quote(str(self.server['db_password']), safe='')
+        host = self.server['host']
+        port = self.server['port']
+
+        # A Unix domain socket directory (as used on the Linux/macOS test
+        # runners) can't be embedded in the URI's authority component: a
+        # "/" there is parsed as the start of the path, not part of the
+        # host, leaving the host/port undetermined and the database name
+        # mangled. libpq's URI form for that case instead leaves the
+        # authority's host empty and passes the socket directory as the
+        # "host" query parameter.
+        if '/' in str(host):
+            return 'postgresql://{0}:{1}@/{2}?host={3}&port={4}'.format(
+                username, password, self.db_name,
+                quote(str(host), safe=''), port)
+
+        return 'postgresql://{0}:{1}@{2}:{3}/{4}'.format(
+            username, password, host, port, self.db_name)
+
+    def _connect(self):
+        return utils.get_db_connection(self.db_name,
+                                       self.server['username'],
+                                       self.server['db_password'],
+                                       self.server['host'],
+                                       self.server['port'],
+                                       self.server['sslmode'])
+
+    def runTest(self):
+        if self.case == 'unreachable':
+            # Port 1 is not something a PostgreSQL server listens on, so the
+            # connection is refused rather than timing out.
+            self.assertFalse(check_external_config_db(
+                'postgresql://pgadmin:pgadmin@127.0.0.1:1/pgadmin'))
+            return
+
+        if self.case == 'malformed':
+            self.assertFalse(check_external_config_db('not a uri at all'))
+            return
+
+        if self.case == 'reachable_without_table':
+            self.assertFalse(check_external_config_db(self._uri()))
+            return
+
+        connection = self._connect()
+        try:
+            old_isolation_level = connection.isolation_level
+            utils.set_isolation_level(connection, 0)
+            cursor = connection.cursor()
+            cursor.execute('CREATE TABLE public.server (id serial)')
+            # Recorded as soon as the table exists, before the isolation
+            # level restore and commit below, so tearDown still drops it
+            # if either of those later steps were to fail.
+            self.created_table = True
+            utils.set_isolation_level(connection, old_isolation_level)
+            connection.commit()
+        finally:
+            connection.close()
+
+        self.assertTrue(check_external_config_db(self._uri()))
+
+    def tearDown(self):
+        if not self.created_table:
+            return
+        connection = self._connect()
+        try:
+            old_isolation_level = connection.isolation_level
+            utils.set_isolation_level(connection, 0)
+            cursor = connection.cursor()
+            cursor.execute('DROP TABLE IF EXISTS public.server')
+            utils.set_isolation_level(connection, old_isolation_level)
+            connection.commit()
+        finally:
+            connection.close()