Over the last week I've been experiencing the exact same issue you described. Big Sur 11.4 and Quantum 4848, but same issue.
After spending hours on it, what eventually resolved it was:
1. Uninstall previous driver
3. Install previous driver version (PreSonus_UniversalControl_v3_4_2_63992) will do
5. Uninstall driver
7. Finally reinstall current driver (3.5). This time I was finally prompted in Security & Privacy to 'Allow' the signed driver. I don't think I was offered this first time round.
8. Wait for install to finish, then go to Security * Privacy > Unlock > Allow.
I know this all seems convoluted but it worked. It seems that only by jumping version numbers in the driver do you get prompted for the 'Allow'.