refactor: Replace RecursiveMutex with Mutex in Shutdown()
Step by step, going to replace all of the RecursiveMutex instances with the Mutex ones throughout the code base :)
Not sure if it is possible in all cases though...
This one is a low-hanging fruit.
This is a backport of core#19180
Test Plan: ninja all check-all
Reviewers: #bitcoin_abc, majcosta
Reviewed By: #bitcoin_abc, majcosta
Differential Revision: https://reviews.bitcoinabc.org/D9279