refactor: remove straggling boost::mutex usage
After the merge of #18710, the linter is warning:
A new Boost dependency in the form of "boost/thread/mutex.hpp" appears to have been introduced:
^---- failure generated from test/lint/lint-includes.sh
the interim #19337 was merged, which introduced more `boost::mutex` usage.
Given we no longer use `boost::mutex`, just remove the double lock test
and remaining includes.