You should definitely run the 10.0.1 BigFix agent on Big Sur regardless of root server version.
I don’t know why this would be specifically. I have run the 9.5 agent on Big Sur and did not have the same issue, but it is also NOT meant to be run on Big Sur. You should proactively upgrade all MacOS devices to 10.0.1 agent as soon as possible to maximize compatibility with Big Sur.
There will be a specific update to the BigFix agent for Big Sur soon, but 10.0.1 should be functional, even if not everything is fully tested and built for Big Sur yet. Once that update is released, you should also upgrade MacOS devices to it as soon as possible.
I am also running 10.0.1 BigFix agent on Apple Silicon on Big Sur using Rosetta 2 emulation. This does seem to work just fine, but the BigFix Self Service application is not working. A native agent for Apple Silicon and updates to the BigFix Self Service Application are in the works to address this, but that will take a bit longer.