How can you retain the original logo if you don’t have the right to use their trademarks?

I'm confused by that as well.

This feels like a sleazy attempt to find a loop hole in the AGPL language to restrict commercial use.

That cannot be the case; OnlyOffice has been working with Nextcloud for years to provide interoperability.

If Only Office doesn’t want people to do this, they could have very easily just chosen a different license from the beginning.

I don't believe that "restricting commercial use" is the problem. In this article OnlyOffice has apparently been having problems with Nextcloud pushing past their licensing boundaries and even soliciting OnlyOffice's customers directly.