

They use a modified version of the AGPL that includes a requirement to use their logo.
They also, in a separate subsection, note that no permission is granted to use their trademarks.
As far as I can tell, the goal is to create a catch-22 that prevents you from forking the project: if you don’t include the logo, they complain that you didn’t include it, and if you include the logo they complain that you’re infringing their trademark.
Edit: Or more specifically, OnlyOffice’s position is that the logo requirement is not a modification because they think it’s an attribution requirement allowed under section 7(b).

You can host through Microsoft, using a service called Minecraft Realms, but the license agreement also entitles you to host your own server using whatever infrastructure you like, with certain restrictions on content and monetization (most notably, you aren’t supposed to include things like gambling and lootboxes using real-world money or MTX currency that can be purchased with real money).
I’m all for piracy, but hosting your own Minecraft server isn’t even piracy, it’s explicitly allowed!