Thanks for helping, phil_m! Your reply led me to do more research yesterday and I saw that Workbench HD 2.14 seemed to work for some people on Big Sur. I tried it, it took a couple of minutes to open, but it works now.
I agree with Charliereilly317, it would be great if the Line 6 guys could chime in here. I've been really happy with my Variax so far, but I use Workbench a lot for custom tunings and if they're not planning on keeping the software updated that could be a dealbreaker for me. A quick search turned up a few more folks who can't use Workbench on Big Sur.