I remember when macOS Big Sur came out people in the programming / comp bio world were saying to avoid installing it as it could cause issues with libraries / dependencies - I think I remember Lior Pachter putting something about it on his Twitter but I can't find the tweet now. Is it OK to go ahead and upgrade, or should I still hold off? I really want to avoid bricking any of my code.
We have no idea what code is important to you. If keeping your code running is a priority (and this is your primary/only machine) then don't upgrade. Apple is generally good about keeping security patches supplied for prior version of the OS so you are covered there. I don't think Big Sur has standout features that make it a must have compared to Catalina.
That said I upgraded a machine in place and recently applied v.11.1 upgrade too.
conda and environments are working fine. You could upgrade after creating a time machine backup. If something breaks after the upgrade, you can always go back to the last version by doing a restore from that backup. Only thing you are likely to lose is time/effort.