[WIP] Investigate keyboard state sync on Windows

[bleroux]

Description

This is a WIP PR to evaluate how #44827 can help to find a solution for flutter/flutter#125975.

This PR makes it a little more difficult to reproduce flutter/flutter#125975 but unfortunately, it does not fix the issue fully.

From my local experimentation, it seems that, with this PR, the engine key pressed state can be updated just after the framework queried the state and before the framework registered key channel handlers (this leads to framework and engine key pressed state being different).

My guess is that this happens because of the async call on the framework side:

    _keyboard.syncKeyboardState().then((_) {
      platformDispatcher.onKeyData = _keyEventManager.handleKeyData;
      SystemChannels.keyEvent.setMessageHandler(_keyEventManager.handleRawKeyMessage);
    });

See https://github.com/flutter/flutter/blob/74e054f04ae59cd9e721710f183f53897b3c9ded/packages/flutter/lib/src/services/binding.dart#L83-L86

Related Issue

Related flutter/flutter#125975

Tests

WIP only

[flutter-dashboard]

This pull request has been changed to a draft. The currently pending flutter-gold status will not be able to resolve until a new commit is pushed or the change is marked ready for review again.

[chinmaygarde]

Triage: Is this stale now?

[bleroux]

Triage: Is this stale now?

Closing because this was an experimental PR I wanted to share with @dkwingsmt.