This is being reported on Adobe forms by various users (link), but Catalina seems to have broken Adobe Illustrator. Users (including myself) report being unable to "Save" new documents or open the "Save As" dialogue box, and the problem persists even when the application is rolled back several releases (23.1.1, 23.1, 23.0.6). The issue, however, seems restricted to MacPros with Touch Bar, as I've spoken iMac users who report upgrading to Catalina without that issue.