Flaky tests TestExecModule/Item_Set_user and TestExecModule/Item_Setting_and_getting_an_user

Examples of failing CI jobs:
* https://github.com/ubuntu/authd/actions/runs/15611824409/job/43974369489
* https://github.com/ubuntu/authd/actions/runs/15642453208/job/44072755005
* https://github.com/ubuntu/authd/actions/runs/15685469571/job/44187418265
```

❌ TestExecModule/Item_Set_user (20ms)
exec_test.go:387: Created service file at /tmp/TestExecModuleItem_Set_user4020967284/002/exec-module
exec_test.go:392:
Error Trace: /home/runner/work/authd-private/authd-private/pam/integration-tests/exec_test.go:392
Error: Not equal:
expected: "an user"
actual : ""

Diff:
--- Expected
+++ Actual
@@ -1 +1 @@
-an user
+
Test: TestExecModule/Item_Set_user
Messages: Item 2 value mismatch
helpers_test.go:328: Could not read artifact "/tmp/TestExecModuleItem_Set_user4020967284/001/exec-module.log": open /tmp/TestExecModuleItem_Set_user4020967284/001/exec-module.log: no such file or directory
❌ TestExecModule/Item_Setting_and_getting_an_user (20ms)
exec_test.go:387: Created service file at /tmp/TestExecModuleItem_Setting_and_getting_an_user3085153475/002/exec-module
exec_test.go:392:
Error Trace: /home/runner/work/authd-private/authd-private/pam/integration-tests/exec_test.go:392
Error: Not equal:
expected: "the-user"
actual : ""

Diff:
--- Expected
+++ Actual
@@ -1 +1 @@
-the-user
+
Test: TestExecModule/Item_Setting_and_getting_an_user
Messages: Item 2 value mismatch
helpers_test.go:328: Could not read artifact "/tmp/TestExecModuleItem_Setting_and_getting_an_user3085153475/001/exec-module.log": open /tmp/TestExecModuleItem_Setting_and_getting_an_user3085153475/001/exec-module.log: no such file or directory
```

Start in pam/integration-tests/exec_test.go at the reported failures around lines 387 and 392, and compare the three linked CI runs. Investigate why Item_Set_user and Item_Setting_and_getting_an_user sometimes return an empty value and why the exec-module log artifact is missing. Done means both tests reliably pass and failure diagnostics remain available.

Written by the indexing model from the issue text.