Here is the breakdown of what you need to know, including which versions work, which don't, and the major issue regarding 32-bit software.
Catalina’s "Auto-Update" and "iCloud Syncing" can hog resources during heavy vector renders. adobe illustrator mac catalina
If you rely on CS6, you must either remain on macOS Mojave or use a virtual machine to run the older operating system. Common Issues and Quick Fixes Here is the breakdown of what you need