This relands https://github.com/flutter/engine/pull/53679.
The difference from the previous attempt is in the last commit, which prevents synthetic focus requests from echoing back into the framework. That part broke too many tests in g3 and needs to be revisited.
## Original description
Stop using `SemanticsAction.didGain/LoseAccessibilityFocus` on the web, start using `SemanticsAction.focus`. This is because on the web, a11y focus is not observable, only input focus is. Sending `SemanticsAction.focus` will guarantee that the framework move focus to the respective widget. There currently is no "unfocus" signal, because it seems to be already covered: either another widget gains focus, or an HTML DOM element outside the Flutter view does, both of which have their respective signals already.
More details in the discussion in the issue https://github.com/flutter/flutter/issues/83809.
Fixes https://github.com/flutter/flutter/issues/83809
Fixes https://github.com/flutter/flutter/issues/148285
Fixes https://github.com/flutter/flutter/issues/143337
d7c9dafda7