Logging screen is leaking with not-GCed _LoggingScreenState, in profile mode.

Follow https://github.com/flutter/devtools/blob/master/packages/devtools_app/lib/src/screens/memory/panes/leaks/LEAK_TRACKING.md for DevTools with disabled inspector screen, in profile mode, connected to the counting app.

Navigate from page to page and resize screens till getting non-GCed leaks in console.

Connect another instance of DevTools to the first one to get the leaks:

```
not-gced:
total: 4820
culprits: 25
victims: 4795
objects:
_LoggingScreenState:
identityHashCode: 706266221
retainingPath:
- /Root-0
- /Isolate-0
- package:flutter/src/widgets/binding.dart/WidgetsFlutterBinding-785502347
- package:flutter/src/widgets/framework.dart/BuildOwner-1134452307
- dart.collection/_InternalLinkedHashMap-0
- dart.core/_List-0
- package:flutter/src/widgets/framework.dart/StatefulElement-89914675
- package:flutter/src/widgets/navigator.dart/NavigatorState-287530411
- dart.core/_GrowableList-0
- dart.core/_List-0
- package:flutter/src/widgets/navigator.dart/_RouteEntry-466314405
- package:flutter/src/material/dialog.dart/DialogRoute-3140187413
- dart.core/_Closure-1712828922
- /Context-797029043
- dart.core/_Closure-4001193036
- /Context-3533831527
- package:devtools_app/src/screens/logging/logging_screen.dart/_LoggingScreenState-706266221
total-victims: 4771
```

```
flutter --version
Flutter 3.0.1-0.0.pre.2590 • channel leak-tracking2 • git@github.com:polina-c/flutter.git
Framework • revision b8c5124e61 (5 hours ago) • 2022-08-26 09:11:08 -0700
Engine • revision 46f80d4196
Tools • Dart 2.19.0 (build 2.19.0-142.0.dev) • DevTools 2.16.0
```