diagnostics: configure diagnostics_log_controller on LoginStatus change

- Add SessionObserver to DiagnosticsLogController.
- Check for OnLoginStatusChanged event to ensure log_base_path_ updated based on the user session.
- Use NoSessionAshTestBase for SessionLogHandler test to ensure ash::Shell is configured for test.
- Test log_base_path_ updates without calling ResetAndInitialize between login type changes.

Bug: b:225191282
Test: Ran ./out/Default/ash_unittests and ./out/Default/ash_webui_unittests. Deployed code to DUT and validated bahavior with and without flag enabled.
Change-Id: Id255a88159a9b3529361249711329b6dc480457d
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3573248
Reviewed-by: Jimmy Gong <jimmyxgong@chromium.org>
Reviewed-by: Gavin Williams <gavinwill@chromium.org>
Commit-Queue: Ashley Prasad <ashleydp@google.com>
Cr-Commit-Position: refs/heads/main@{#994419}