I also attempted to create a new recordset from the Horizon web interface (in the svc.data-engineering.eqiad1.wikimedia.cloud zone) but I got an error, so I'm not sure whether or not that is supposed to work.

Which error did you get? Self-service creation in Horizon is indeed the intended way here.

Thanks @Majavah

I just get a simple hover box popping up, saying Error: Unable to create the record set.

I'm intriged as to why the domain data-engineering.eqiad1.wikimedia.cloud doesn't show up in the list of domains that I can edit in Horizon.
I'm happy to add the record to the .svc. subdomain though (or any other if you say that's correct).

Try specifying the fully qualified record name in the "name" box, so mysql-rw.svc.data-engineering.eqiad1.wikimedia.cloud..

I'm intriged as to why the domain data-engineering.eqiad1.wikimedia.cloud doesn't show up in the list of domains that I can edit in Horizon.

I believe this is because we have a few scripts that would get confused if host records were mixed with others in the same zone. (I may be totally wrong here). Technically they're defined in the cloudinfra project.

Try specifying the fully qualified record name in the "name" box, so mysql-rw.svc.data-engineering.eqiad1.wikimedia.cloud..

That worked a treat. Many thanks indeed.