I just got a new Mac Mini M1, and I am getting the "an error occurred when attempting to change modules" error. There are two recommended approaches to fix this and neither work: 1) delete plist file and restart. Why it doesn't work: The instructions for locating the plist file are for Lightroom Classic, not CC. I cannot locate the plist file for Lightroom CC. 2) Uninstall Lightroom in Creative Cloud and reinstall. Why it doesn't work: The option to uninstall is not there for Lightroom.
Sorry that you're getting an error "an error occurred when attempting to change modules" while loading Lightroom on your new Mac Mini M1.
Would you mind sharing the version of Lightroom you are using? Since you cannot launch the app, provide a screenshot of the app in the Creative Cloud Desktop app or post a screen grab of the above error message.