'Filter by tag' is disabled even if user tags are printed.

Steps:

1. Get DevTools at https://github.com/flutter/devtools/pull/8138
2. set DebugTimer.snapshot to DebugTimer()
3. Run DevTools in debug mode on mac:
flutter run --debug -d macos
4. Connect to an app (counter?) on macos
5. In CLI console find link for the connected DevTools, open it and:
* Select the tab CPU Profile
* Click ‘Start recording’
6. In first DevTools take memory snapshot
7. See in console that user tag is started
8. In second DevTools click ‘Stop’
9. Find ‘Filter by tag: none’ is disabled

Reproduce the issue using the listed macOS CPU Profile and memory-snapshot steps, starting with the CLI console's user-tag output and the CPU Profile 'Filter by tag' control. Trace why the control remains disabled after the tag is printed; done means the filter is enabled when a user tag is available and remains disabled when none exists.

索引モデルが issue の本文から書いたものです。