DevTools integration test flakes

[elliette]

Some of our integration tests have recently become quite flaky. Looking at the past failures on master:

integration_test/test/live_connection/service_extensions_test.dart

• example: https://github.com/flutter/devtools/actions/runs/9767563965/job/26963163313
• failure message:

A SemanticsHandle was active at the end of the test.
All SemanticsHandle instances must be disposed by calling
dispose() on the SemanticsHandle.

integration_test/test/live_connection/debugger_panel_test.dart

*example: https://github.com/flutter/devtools/actions/runs/9717510192/job/26823396168

• failure message:

Actual: _TextWidgetFinder:<Found 0 widgets with text
"package:flutter_app/src/other_classes.dart": []>
Which: means none were found but one was expected

integration_test/test/live_connection/eval_and_inspect_test.dart

• example: https://github.com/flutter/devtools/actions/runs/9716615461/job/26820586270
• failure message:

Actual: _TextContainingWidgetFinder:<Found 0 widgets with text
containing Variable button is created : []>
   Which: means none were found but one was expected

• another example: https://github.com/flutter/devtools/actions/runs/9705257826/job/26787029069
• failure message:

Actual: _TextWidgetFinder:<Found 0 widgets with text "55": []>
Which: means none were found but one was expected