The license isn't the issue. It's the User Agreement. Bambu is claiming that the fork is allowing, enabling, (and/or promoting, encouraging, etc) users to violate the agreement with Bambu to not use their cloud with third party software.
I'm fairly certain user agreements have been used for suing makers of game cheats and other similar things. Certainly in the industry I work in, there was a company making third party software and integrating it with the industry standard tool without going through the official channels, which caused people to violate the user agreement when used. They got sued and settled.
Even with a user agreement I think they need to gate their service behind that agreement, otherwise the agreement is optional and open ports are open for use.
You still need to form a valid contract - no notice, no assent, no contract.
If there's a gate that's being bypassed then this all changes but it doesn't seem like there is - and it doesn't seem like they can add one without breaking existing printers.
From the AGPL:
>When you convey a covered work, you waive any legal power to forbid circumvention of technological measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the work's users, your or third parties' legal rights to forbid circumvention of technological measures.