I'm also having this issue, I installed MAMP as a temporary work around which seemed to start the processes for Ampps to "work" again though I couldn't open the program window. However, I then had a system message telling me my mac had run out of memory with Ampps taking up 60gb so there seems to be some memory leak also with the app after the Big Sur update. If anyone finds a solution please post it as I'm desperate to get this up and running again, thanks!