Lots of test errors with Python 3.13

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## Description



I'm packaging jupyter-server for Debian, and we've just run the tests with Python 3.13.  Unfortunately many of them gave errors, all with a ResourceWarning.  Here are two examples of such errors; attached is a full log (only the start of the error is shown here).



```

228s _ ERROR at setup of test_authorized_requests[True-POST-/api/sessions-{"path": "foo", "type": "bar"}] _

228s 

228s >       lambda: ihook(item=item, **kwds), when=when, reraise=reraise

228s     )

228s E   pytest.PytestUnraisableExceptionWarning: Exception ignored in: <sqlite3.Connection object at 0x7fc6b6048310>

228s E   

228s E   Traceback (most recent call last):

228s E     File "<frozen os>", line 713, in __getitem__

228s E   KeyError: b'COLUMNS'

228s E   

228s E   During handling of the above exception, another exception occurred:

228s E   

228s E   Traceback (most recent call last):

228s E     File "<frozen os>", line 716, in __getitem__

228s E   ResourceWarning: unclosed database in <sqlite3.Connection object at 0x7fc6b6048310>

228s 

228s ihook      = <HookCaller 'pytest_runtest_setup'>

228s item       = <Function test_authorized_requests[True-POST-/api/sessions-{"path": "foo", "type": "bar"}]>

228s kwds       = {}

228s 

228s /usr/lib/python3/dist-packages/flaky/flaky_pytest_plugin.py:146: PytestUnraisableExceptionWarning

```

and

```

228s _ ERROR at setup of test_get_nb_contents[FileContentsManager-unicod\xe9-innonascii] _

228s 

228s >       lambda: ihook(item=item, **kwds), when=when, reraise=reraise

228s     )

228s E   pytest.PytestUnraisableExceptionWarning: Exception ignored in: <sqlite3.Connection object at 0x7fc6b670d4e0>

228s E   

228s E   Traceback (most recent call last):

228s E     File "/usr/lib/python3/dist-packages/yaml/resolver.py", line 143, in resolve

228s E       def resolve(self, kind, value, implicit):

228s E       

228s E   ResourceWarning: unclosed database in <sqlite3.Connection object at 0x7fc6b670d4e0>

228s 

228s ihook      = <HookCaller 'pytest_runtest_setup'>

228s item       = <Function test_get_nb_contents[FileContentsManager-unicod\xe9-innonascii]>

228s kwds       = {}

228s 

228s /usr/lib/python3/dist-packages/flaky/flaky_pytest_plugin.py:146: PytestUnraisableExceptionWarning

```

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- Operating System and version: Debian testing with python3-defaults from unstable (supporting Python 3.13)

- Browser and version: N/A

- Jupyter Server version: 2.14.2

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