EDIT: Turns out, I had forgotten DMARC records, and in a scatterbrained state, of course the first few mails went through when I tested, so I assumed, everything is going well. Testing now seems to indicate Gmail is accepting the automatic mails again - please report if you end up noticing issues.
Gmail has started rejecting mail from my mail server - even though I have definitely set up DKIM and other records properly, and they had been getting accepted there before.
For this reason, please use a different mail provider until further notice, when signing up. As long as volume is manageable, I will try to forward the mail to Gmail addresses by hand myself - but this will always have some delay, and is not guaranteed to continue.
I have started an appeal through their system, after I checked that I indeed should be fulfilling all they need on their checklist for incoming mail.
Ah, this is a bit embarrassing, because I think you’re right - I was sure I set it up, but I must have forgotten because something else needed fixing - and then while testing, of course the first few automatic mails and test mails I sent by hand went through without a hitch. Interestingly, that was not being asked in the checklist I went through for Gmail.
Thank you - that should be something I can do!