Per Deon (ALTERANT) via DOVE-Net:

Oct  7 09:47:16 d-11-1 synchronet: srvc 0060 BINKPS connection accepted from:
2402:1f00:8101:b3c:1000::2 port 55338
Oct  7 09:47:16 d-11-1 synchronet: srvc 0060 BINKPS TLS ERROR 'Server
certificate has expired' (-3) setting private key
Oct  7 09:47:16 d-11-1 synchronet: srvc 0060 BINKPS TLS ERROR 'Data has not
been initialised' (-11) setting session active

Which was odd, because my cert was renewed.

I forced renewed it, and confirmed it was valid, but they were still failing.

I noticed that letsyncrypt only recycles the web, which is probably the issue.
Once I recycled everything, binkps connections started working again.