I googled the error code I was receiving in my logs:
Access denied with code 418 (phase 2)
It’s coming from my hosts (DreamHost). I disabled their mod_security firewall and that seems to have down the trick. See their documentation here.
I’m going to contact them first to let them know about the issue and see what they say. It would probably be a good idea to let the Twenty Twenty Three forums know as well, even though it’s unclear whether it’s something to do with the theme.
I’ll update this thread with any further info as it comes.