```
Also, add lock annotation to SendMessages
Can be reviewed with "--word-diff-regex=."
```
Completes backport of [[https://github.com/bitcoin/bitcoin/pull/20864 | core#20864]]:
https://github.com/bitcoin/bitcoin/pull/20864/commits/fa210689e27b0d78b2fe894e51e364179db7a3ce
Depends on D10880.
Ref T1696.