Flutter web integration tests failing

Example failure: https://github.com/flutter/devtools/actions/runs/9019966240/job/24787570258?pr=7731

This reproduces on the master branch locally: `dart run integration_test/run_tests.dart --target=integration_test/test/live_connection/debugger_panel_test.dart --test-app-device=chrome`

Failure logs from local run (failure occurs after performing a hot restart):
```
FlutterDriveProcess - Launching integration_test/test/live_connection/debugger_panel_test.dart on Chrome in debug mode...
FlutterDriveProcess - Waiting for connection from debug service on Chrome...
FlutterDriveProcess - Warning: In index.html:55: Local variable for "serviceWorkerVersion" is deprecated. Use "{{flutter_service_worker_version}}" template token instead.
FlutterDriveProcess - Warning: In index.html:92: "FlutterLoader.loadEntrypoint" is deprecated. Use "FlutterLoader.load" instead.
FlutterDriveProcess - Warning: In index.html:113: "FlutterLoader.loadEntrypoint" is deprecated. Use "FlutterLoader.load" instead.
FlutterDriveProcess - Waiting for connection from debug service on Chrome... 68.5s
FlutterDriveProcess - This app is linked to the debug service: ws://127.0.0.1:52704/B6InlRhbaIo=/ws
FlutterDriveProcess - Debug service listening on ws://127.0.0.1:52704/B6InlRhbaIo=/ws
FlutterDriveProcess - 00:00 +0: (setUpAll)
FlutterDriveProcess - 00:00 +1: Debugger panel
ChromeDriver - [1715275866.798][WARNING]: This version of ChromeDriver has not been tested with Chrome version 124.
FlutterDriveProcess - devtools server not available (200)
FlutterDriveProcess - DevTools version 2.36.0-dev.6.
FlutterDriveProcess - No DTD uri provided from the server during initialization.
FlutterDriveProcess - DevTools log level changed to INFO
FlutterDriveProcess - TEST STATUS: connecting to test app
FlutterDriveProcess - Attempted to call extension 'ext.flutter.inspector.structuredErrors', but no service with that name exists
FlutterDriveProcess - readyToResume: (106) Can only perform operation while paused.
FlutterDriveProcess - getSourceReport: (-32602) Source report kind Coverage not supported
FlutterDriveProcess - TEST STATUS: switching to debugger screen (icon IconData(U+0F112))
FlutterDriveProcess - TEST STATUS: looking for the main.dart file
FlutterDriveProcess - TEST STATUS: Navigating to line 57...
FlutterDriveProcess - TEST STATUS: opening the "more" menu
FlutterDriveProcess - Semantic node 261 had both scopesRoute and namesRoute set, indicating a self-labelled dialog, but it is missing the label. A dialog should be labelled either by setting namesRoute on itself and providing a label, or by containing a child node with namesRoute that can describe it with its content.
FlutterDriveProcess - Semantic node 261 had both scopesRoute and namesRoute set, indicating a self-labelled dialog, but it is missing the label. A dialog should be labelled either by setting namesRoute on itself and providing a label, or by containing a child node with namesRoute that can describe it with its content.
FlutterDriveProcess - Semantic node 261 had both scopesRoute and namesRoute set, indicating a self-labelled dialog, but it is missing the label. A dialog should be labelled either by setting namesRoute on itself and providing a label, or by containing a child node with namesRoute that can describe it with its content.
FlutterDriveProcess - TEST STATUS: selecting the go-to-line menu option
FlutterDriveProcess - TEST STATUS: entering line number 57 in the go-to-line dialog
FlutterDriveProcess - TEST STATUS: looking for line 57
FlutterDriveProcess - TEST STATUS: setting a breakpoint
FlutterDriveProcess - TEST STATUS: performing a hot restart
FlutterDriveProcess - getSourceReport: (-32602) Source report kind Coverage not supported
FlutterDriveProcess - readyToResume: (106) Can only perform operation while paused.
FlutterDriveProcess - result {"result":"false","failureDetails":["{\"methodName\":\"Debugger panel\",\"details\":\"══╡ EXCEPTION CAUGHT BY FLUTTER TEST FRAMEWORK ╞═════════════════\\nThe following TestFailure was thrown running a test:\\nExpected: exactly one matching candidate\\n Actual: _TextContainingWidgetFinder:\\n Which: means none were found but one was expected\\n\\nWhen the exception was thrown, this was the stack:\\ndart-sdk/lib/_internal/js_dev_runtime/private/ddc_runtime/errors.dart 296:3 throw_\\npackages/matcher/src/expect/expect.dart 149:31 fail\\npackages/matcher/src/expect/expect.dart 144:3 _expect\\npackages/matcher/src/expect/expect.dart 56:3 expect$\\npackages/flutter_test/src/widget_tester.dart 474:18 expect$\\ndebugger_panel_test.dart 208:3 goToLine\\ndart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 45:50 \\ndart-sdk/lib/async/zone.dart 1407:47 _rootRunUnary\\ndart-sdk/lib/async/zone.dart 1308:19 runUnary\\ndart-sdk/lib/async/future_impl.dart 163:18 handleValue\\ndart-sdk/lib/async/future_impl.dart 847:44 handleValueCallback\\ndart-sdk/lib/async/future_impl.dart 876:13 _propagateToListeners\\ndart-sdk/lib/async/future_impl.dart 652:5 [_completeWithValue]\\ndart-sdk/lib/async/future_impl.dart 722:7 \\ndart-sdk/lib/async/zone.dart 1399:13 _rootRun\\ndart-sdk/lib/async/zone.dart 1301:19 run\\ndart-sdk/lib/async/zone.dart 1209:7 runGuarded\\ndart-sdk/lib/async/zone.dart 1249:23 callback\\ndart-sdk/lib/async/schedule_microtask.dart 40:11 _microtaskLoop\\ndart-sdk/lib/async/schedule_microtask.dart 49:5 _startMicrotaskLoop\\ndart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 181:7 \\n\\nThe test description was:\\n Debugger panel\\n═════════════════════════════════════════════════════════════════\\n\"}"]}
FlutterDriveProcess - Failure Details:
FlutterDriveProcess - Failure in method: Debugger panel
FlutterDriveProcess - ══╡ EXCEPTION CAUGHT BY FLUTTER TEST FRAMEWORK ╞═════════════════
FlutterDriveProcess - The following TestFailure was thrown running a test:
FlutterDriveProcess - Expected: exactly one matching candidate
FlutterDriveProcess - Actual: _TextContainingWidgetFinder:
FlutterDriveProcess - Which: means none were found but one was expected
FlutterDriveProcess -
FlutterDriveProcess - When the exception was thrown, this was the stack:
FlutterDriveProcess - dart-sdk/lib/_internal/js_dev_runtime/private/ddc_runtime/errors.dart 296:3 throw_
FlutterDriveProcess - packages/matcher/src/expect/expect.dart 149:31 fail
FlutterDriveProcess - packages/matcher/src/expect/expect.dart 144:3 _expect
FlutterDriveProcess - packages/matcher/src/expect/expect.dart 56:3 expect$
FlutterDriveProcess - packages/flutter_test/src/widget_tester.dart 474:18 expect$
FlutterDriveProcess - debugger_panel_test.dart 208:3 goToLine
FlutterDriveProcess - dart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 45:50
FlutterDriveProcess - dart-sdk/lib/async/zone.dart 1407:47 _rootRunUnary
FlutterDriveProcess - dart-sdk/lib/async/zone.dart 1308:19 runUnary
FlutterDriveProcess - dart-sdk/lib/async/future_impl.dart 163:18 handleValue
FlutterDriveProcess - dart-sdk/lib/async/future_impl.dart 847:44 handleValueCallback
FlutterDriveProcess - dart-sdk/lib/async/future_impl.dart 876:13 _propagateToListeners
FlutterDriveProcess - dart-sdk/lib/async/future_impl.dart 652:5 [_completeWithValue]
FlutterDriveProcess - dart-sdk/lib/async/future_impl.dart 722:7
FlutterDriveProcess - dart-sdk/lib/async/zone.dart 1399:13 _rootRun
FlutterDriveProcess - dart-sdk/lib/async/zone.dart 1301:19 run
FlutterDriveProcess - dart-sdk/lib/async/zone.dart 1209:7 runGuarded
FlutterDriveProcess - dart-sdk/lib/async/zone.dart 1249:23 callback
FlutterDriveProcess - dart-sdk/lib/async/schedule_microtask.dart 40:11 _microtaskLoop
FlutterDriveProcess - dart-sdk/lib/async/schedule_microtask.dart 49:5 _startMicrotaskLoop
FlutterDriveProcess - dart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 181:7
FlutterDriveProcess -
FlutterDriveProcess - The test description was:
FlutterDriveProcess - Debugger panel
FlutterDriveProcess - ═════════════════════════════════════════════════════════════════
```