I worded that poorly.

Yes, that is of course correct. But that means that your clients have to trust you without technical safeguards, that you will not use this to get for certificates for purposes other than XMPP.

Which, in my mind, is a problem if the domain is not used just for XMPP, but lets say for a website as well.

You should be able to do that via DNS SRV entries.

  _xmpp-client._tcp.domain.tld. TTL IN SRV priority weight port target
  _xmpps-client._tcp.domain.tld. TTL IN SRV priority weight port target

  example:
  _xmpp-client._tcp.not-my-domain.com. 3599 IN SRV 5 0 5222 jabber.my-domain.com.

I don't think I have seen a client complain about the cert being for jabber.my-domain.com Which one is giving trouble there?

source: https://datatracker.ietf.org/doc/html/rfc6120

https://wiki.xmpp.org/web/SRV_Records