From the blog:

ONLYOFFICE is distributed under the GNU Affero General Public License v3 (AGPL v3)

And

preserving ONLYOFFICE branding in derivative works;

IDK seems to me it's not really GPL if you can't fork it, and that clause is certainly not compatible with any other GPL code.

If they use any GPL code they are probably in violation of that license.
Looks to me like they want to appear opensource, while keeping control of the code?

ensure a balance between openness of the code and protection of the rights of the copyright holder.

Yep there it is, this is completely contradictory to how GPL 3 works. You can't call it GPL3 and at the same time claim the copyright.
ONLYOFFICE is completely misunderstanding how AGPL works.

https://en.wikipedia.org/wiki/GNU_Affero_General_Public_License

The main purpose of AGPL was to facilitate the use of GPL for online services, which wasn't really possible to make with older GPL versions, because they require distribution of the source code together with the software.

The AGPL license allows the license holder to specify additional terms of the license that require preservation of specified reasonable attributions or legal notices - this is covered in 7B, and the onlyoffice license specifies that the logo must be preserved for attribution.

Assuming a logo legally counts as reasonable attribution (IANAL) that would put only office in the right here, but holy shit, the fact that the license allows these modifications to be put on line #655 rather than line #2 is absurd. I, like most people I assume, only read far enough into the license to figure out whether it's MIT or GPL

I did a cursory glance at their GitHub repos - all the ones that state the license terms of the repo are AGPL, Apache or MIT, with one exception - BSD.

So I don't really get what "licensing terms" are being violated here.

this what happens when being truly open source isn't prioritised.