http: simplify parser lifetime tracking

Instead of providing a separate class for keeping the
parser alive during its own call back, just delay a
possible `.close()` call until the stack has cleared
completely.

PR-URL: https://github.com/nodejs/node/pull/18135


Reviewed-By: James M Snell <jasnell@gmail.com>
Reviewed-By: Franziska Hinkelmann <franziska.hinkelmann@gmail.com>
Reviewed-By: Anatoli Papirovski <apapirovski@mac.com>
Reviewed-By: Colin Ihrig <cjihrig@gmail.com>