You seem to be conflating the DMCA, which regulates copying of copyrighted material, and the CFAA, which criminalizes unauthorized access.
I don't think there is any case law related to "which client was used" applications of the CFAA.
I can't really imagine any reasonable circumstance where someone would be authorized with one client and unauthorized with another. It's not really a reasonable position; if you offer a free network service on the internet, and anyone is authorized to use it, I don't know of any legal basis for gating that authorization on "user of your software".
Perhaps some internet-clueless judge will one day disagree, but that's not how the mores and norms of the internet work today. Signal doesn't get to declare me a criminal if I write my own client software to talk to the Signal API servers (or use some other open source software I found), regardless of Moxie's squeaking. Either your service is public and open to everyone, or it isn't.
This is reminiscent of anti-scraping lawsuits: "you may only access LinkedIn using the LinkedIn web application; it is a violation to access it using curl". Ironically, Google's position in that regard is likely to bite them here, where someone else wants to use unconventional clients.
I don't think there is any case law related to "which client was used" applications of the CFAA.
I can't really imagine any reasonable circumstance where someone would be authorized with one client and unauthorized with another. It's not really a reasonable position; if you offer a free network service on the internet, and anyone is authorized to use it, I don't know of any legal basis for gating that authorization on "user of your software".
Perhaps some internet-clueless judge will one day disagree, but that's not how the mores and norms of the internet work today. Signal doesn't get to declare me a criminal if I write my own client software to talk to the Signal API servers (or use some other open source software I found), regardless of Moxie's squeaking. Either your service is public and open to everyone, or it isn't.