Unmodified, modified, whatever.
I don’t think that was your intent, but that’s exactly how it reads. Or maybe that is your intent?
Why do you think the GPL is not compatible with this?
Plus, they can always offer other licenses in addition to the GPL (or really AGPL would be a better fit for their concerns). It’s their software, so they can license it to anyone with whatever terms they want. (Assuming there aren’t outside contributions, but even that can be dealt with)
Yep, that's exactly what I was thinking. They're clearly offering alternative licenses to the one in the public repository. There is no reason the same tactic couldn't be applied with the GPL.
To prevent paid sync services, you should license your protocols and data formats in AGPL, which requires derivative work (third-party sync services) to be open sourced.
The client app in contrast, should be fine even in permissive licenses.