I just got deeper into the problem, and it's not a Dropbox problem (it was an interpretation error).
However, I was right with my first impression: It is related to code sign re-inforcement done by Apple on the ARM64 architecture.
It is mandatory to code sign every app that runs on M1, so now I have to check if some kind of "ad-hoc" signature is valid for the binary sharing.
In the meantime, the Intel version through Rossetta2 can be used, because this tight rules imposed by Apple do not apply to x86_64 architecture (regardless if the machine runs Big Sur or not).