[Flaky integration test] `packages/devtools_app/integration_test/test/live_connection/service_extensions_test.dart`: "A SemanticsHandle was active at the end of the test."

Splitting this issue out of https://github.com/flutter/devtools/issues/8013 to handle this particular test flake for the [`service_extensions_test`](https://github.com/flutter/devtools/blob/master/packages/devtools_app/integration_test/test/live_connection/service_extensions_test.dart).

DevTools itself never creates a `SemanticsHandler`, so I'm guessing this failure is actually coming from the framework. Possibly related to https://github.com/flutter/flutter/issues/121640

Unfortunately I've been unable to reproduce this while running locally, though we have been hitting this during CI testing.

Example test runs:
* https://github.com/flutter/devtools/actions/runs/10097795429/job/27923501767
* https://github.com/flutter/devtools/actions/runs/9767563965/job/26963163313

Failure message:
```
Failure Details:
Failure in method: can call services and service extensions
══╡ EXCEPTION CAUGHT BY FLUTTER TEST FRAMEWORK ╞═════════════════
The following assertion was thrown running a test (but after the
test had completed):
A SemanticsHandle was active at the end of the test.
All SemanticsHandle instances must be disposed by calling
dispose() on the SemanticsHandle.

When the exception was thrown, this was the stack:
dart-sdk/lib/_internal/js_dev_runtime/private/ddc_runtime/errors.dart 296:3 throw_
packages/flutter_test/src/test_text_input_key_handler.dart.js 10314:19 [_verifySemanticsHandlesWereDisposed]
packages/flutter_test/src/test_text_input_key_handler.dart.js 10308:50 [_endOfTestVerifications]
packages/flutter_test/src/test_text_input_key_handler.dart.js 11295:11 _runTestBody
dart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 47:50
dart-sdk/lib/async/zone.dart 1407:47 _rootRunUnary
dart-sdk/lib/async/zone.dart 1308:19 runUnary
dart-sdk/lib/async/future_impl.dart 163:18 handleValue
dart-sdk/lib/async/future_impl.dart 861:44 handleValueCallback
dart-sdk/lib/async/future_impl.dart 890:13 _propagateToListeners
dart-sdk/lib/async/future_impl.dart 666:5 [_completeWithValue]
dart-sdk/lib/async/future_impl.dart 736:7
dart-sdk/lib/async/zone.dart 1399:13 _rootRun
dart-sdk/lib/async/zone.dart 1301:19 run
dart-sdk/lib/async/zone.dart 1209:7 runGuarded
dart-sdk/lib/async/zone.dart 1249:23 callback
dart-sdk/lib/async/schedule_microtask.dart 40:11 _microtaskLoop
dart-sdk/lib/async/schedule_microtask.dart 49:5 _startMicrotaskLoop
dart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 183:7
═════════════════════════════════════════════════════════════════

#0 IntegrationTestRunner.run.runTest (package:devtools_shared/src/test/integration_test_runner.dart:138:11)

#1 IntegrationTestRunner.run (package:devtools_shared/src/test/integration_test_runner.dart:143:5)

#2 runFlutterIntegrationTest (file:///Users/runner/work/devtools/devtools/packages/devtools_app/integration_test/test_infra/run/run_test.dart:66:5)

#3 _runTest (file:///Users/runner/work/devtools/devtools/packages/devtools_app/integration_test/run_tests.dart:81:3)

#4 runOneOrManyTests (package:devtools_shared/src/test/integration_test_runner.dart:330:9)

#5 main (file:///Users/runner/work/devtools/devtools/packages/devtools_app/integration_test/run_tests.dart:53:3)

```