inspector: code cleanup

1. Do not rely on a string comparison to identify when
   the frontend is ready to run and override a callback instead.
2. Remove unused boolean flag.

PR-URL: https://github.com/nodejs/node/pull/27591


Reviewed-By: Anna Henningsen <anna@addaleax.net>
Reviewed-By: Aleksei Koziatinskii <ak239spb@gmail.com>