Cloud + a probably similar method, but, the process the author used is not efficient in figuring out the private frameworks work. You could do a few things I think that would allow you to debug the framework calls & iMessage itself to understand what is actually going on / how it’s used.

I'm curious if they have a farm of iPhones somewhere to host this off of. They are sending the iMessages from phone numbers -- not email addresses, which means they didn't just get a bunch of Mac Minis and do it the (probably easier) way.

Jailbroken iPhones where you can automate the UI and (maybe?) access any private Messaging API Apple left laying around would make this scalable though.

The phone farm has to be the approach. I don’t see any other way.

Guessing that they are using Apple Business Chat. We've looked at using it, too.

Apple Business Chat doesn't seem to be Blue though, at least in my experience with Apple Card Support. Messages seem to be Black, unless that's exclusive to talking with Apple (maybe businesses can have configurable color schemes).