Cleaner Professional Mac Hangs for both Analysis and Cleaning

version 1.18.30 on intel big sur.

the app launches but fails to start analysis or cleaner mode. Progress stays at 0%

Did you look into the thread that was updated shortly before your post:

Additionally, we've had some users reporting that simply allowing the program to run for several minutes or longer will allow it to progress.

Improving compatibility with Big Sur is one of the things being looked into for the CCleaner for Mac 2.0 project.