doc: improve text in async_hooks.md

* Remove unnecessary *Note:* designations.
* Various small edits for tone, punctuation, etc.

PR-URL: https://github.com/nodejs/node/pull/19312


Reviewed-By: Vse Mozhet Byt <vsemozhetbyt@gmail.com>
Reviewed-By: Colin Ihrig <cjihrig@gmail.com>
Reviewed-By: James M Snell <jasnell@gmail.com>