Hi David,
I experienced the same bug on my config (Moodle 3.7.1, Apache load balancer, 3 apache worker, 1 dedicated DB server, 1 dedicated Redis server, and data via NFS, fordson theme).
It was impossible to upload any file anywhere or to edit a theme announce and a simple purge of alla cache files did the trick.
Looks like there is a mutex or synchronicity problem somewhere on some cache file types.
Thanks,
Francis