I'm here looking at whether to update from Mojave to Big Sur. EyeTV has been a major stumbling block as it appears v4 is no good and I stream to my iPad every day as well.
Can you explain how you installed and got, presumably, Mojave running under Catalina in Parallels? Did you copy your pre-upgraded System to Parallels or did you have to install a basic OS then reinstall all the applications you want to run. I've still got a ton of 32-bit apps I really don't want to lose and it would really help not to have to find the installers, codes and reinstall them all. I bet most of the old updates aren't available any more as well.