Well, I checked SMTP submission on my grommunio install and now I remember, what my problem was: my Mac - and probably no SMTP client, is able to authenticate against SMTP submission, since the install lacks saslauthd as stated in the logs:
[2022-05-28 14:56:15.279932]: warning: SASL authentication failure: cannot connect to saslauthd server: No such file or directory
[2022-05-28 14:56:15.280092]: warning: budysmbp.stephanbudach.de[10.10.0.106]: SASL LOGIN authentication failed: generic failure
If this is an error in my installation, I'll happily create a separate thread for it, but I remembered to wait for full EWS support since, that would spare me the effort of setting up saslauth on my own. Plus that way, the user credentials would have to be managed twice, which I was also not looking forward to.