Flaky test TestGdmModel

I'm seeing both

```
TestGdmModel/Authenticated_with_preset_PAM_user_updated_and_server_side_broker_and_authMode_selection`
```

and

```
TestGdmModel/Authenticated_after_auth_selection_stage_from_client_after_client_side_broker_and_auth_mode_selection_if_there_is_only_one_auth_mode
```

fail very frequently in the `autopkgtest` CI jobs:

* https://github.com/ubuntu/authd/actions/runs/17977117879/job/51134399827?pr=1087#step:4:34788
* https://github.com/ubuntu/authd/actions/runs/18007390035/job/51231956033?pr=1091#step:4:34823
* https://github.com/ubuntu/authd/actions/runs/18007390035/job/51231956030?pr=1091#step:4:34360
* https://github.com/ubuntu/authd/actions/runs/18007390035/job/51231956009?pr=1091#step:4:34089

Start with the named TestGdmModel subtests and the linked autopkgtest CI job logs, then reproduce the failures in the same CI environment. Trace why these two cases are nondeterministic and verify that both pass reliably across repeated autopkgtest runs.

Written by the indexing model from the issue text.