I'm not sure what might be causing the error, but here are some things to try. You can pass a -v argument to the downloader like this to enable verbose output, which might help figure out the cause of the problem:
Hello, for me even the rustup-init failed. Finally I found that Ubuntu offered me installing two different versions of curl with apt or snap. I first chose snap to install it, then I got the error message. When I removed the snap version and installed curl with apt, the rust install worked without any problem.
That is definitely possible.
I've heard complaints before about how snap, flatpak and the like break all sorts of assumptions that regular applications make, in the process making them next to useless as a packaging mechanism for those applications (that's irony for ya: an entire generation of package managers that has simply made itself obsolete before it even became workable).
If it is that, then installing rust using the regular shell script should be able to so le this issue.