Relands #34363 which was reverted in #36091 with fix.

Fix flutter/flutter#110867. The fix is in 6cf5494; the parent commit is a pure revert of the revert.

Explanation of flutter/flutter#110867

Some user might write Dart code like the following to keep the app in full screen mode even after this might be changed in response to certain user actions. There is no built in time out or gesture that will restore the full screen mode the app was in. (Thanks to @Piinks for helping me understand this offline)

SystemChrome.setSystemUIChangeCallback((systemOverlaysAreVisible) async {
  SystemChrome.restoreSystemUIOverlays();
});

This is what happens:

1. User swipes up or does some gesture which causes the system UI mode to change
2. OnSystemUiVisibilityChangeListener receives a notification of the change
3. It propagates a platform message to Dart; the Dart callback defined in setSystemUIChangeCallback (above) is called
4. SystemChrome.restoreSystemUIOverlays() is called in the callback, sending a platform message to the host
5. Platform message is scheduled on the host; resulting in a call to setSystemUiVisibility.

1-5 all occur in the same frame. Because of this, OnSystemUiVisibilityChangeListener will silently stop responding to future system UI notifications.

#34363 introduces the behaviour in bold; previously using new Handler instead of Handler.createAsync will always cause platform messages to be scheduled in the next frame, such as in (5).

This PR causes (3) to be scheduled in a subsequent frame, avoiding the issue.

Pre-launch Checklist

• I read the [Contributor Guide] and followed the process outlined there for submitting PRs.
• I read the [Tree Hygiene] wiki page, which explains my responsibilities.
• I read and followed the [Flutter Style Guide] and the [C++, Objective-C, Java style guides].
• I listed at least one issue that this PR fixes in the description above.
• I added new tests to check the change I am making or feature I am adding, or Hixie said the PR is test-exempt. See [testing the engine] for instructions on
  writing and running engine tests.
• I updated/added relevant documentation (doc comments with ///).
• I signed the [CLA].
• All existing and new tests are passing.

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