The current release of Geneious Prime (2020.2.4) has a known stability issue on Big Sur so we recommend not upgrading at this time. Specifically, Geneious Prime may experience crashes if the computer is allowed to sleep or Geneious is idle for an extended period of time.
The upcoming Geneious Prime 2021 release has one known issue running on MacOS 11.0 Big Sur. This is related to the Find CRISPR Sites operation, where the Doench et al 2016 algorithm to calculate Activity Scores is not currently able to be run on Big Sur. There are no other known issues.
The beta release of Prime 2021 is available here.