Most likely some work would be needed to accommodate the UI changes made to Finder in Big Sur. Not sure if the core of Finder has changed much or not but I kinda doubt it has.
I’m 100% sure given some time TotalFinder can be updated to support Big Sur since I’ve already demonstrated my own implementation of one of the features (colored sidebar).
It’s unlikely anything needs to change about the injection method aside from requiring users to run without Library Validation. Although personally I’d probably switch away from using .osax scripting to load I don’t think it inherently presents any problems.