I've noticed mail sending seems to have two '535 Incorrect authentication data' lines which I see on other mail attempts also. Looks like we issue two bad attempts then the third works.

Mythic Beasts have investigated and replied:

I think this is down to /etc/exim4/passwd.client. This contains:

mx.mythic-beasts.com::

so Exim must be trying to authenticate with blank credentials and this obviously fails.

Looking in etckeeper, this was added on the 17th of March, and the file also has a comment to say it's managed by Chef. Prior to this, it was the default file, which is blank except for comments.

I think if you remove this entry, that should make those errors go away.