Is PopChar compatible with macOS Ventura?

Yes, in general the current version 9.4 of PopChar runs on macOS Ventura.

We are in the process of preparing a maintenance release that irons out some small Ventura compatibility issues and will release a beta of PopChar 9.5 soon. We recommend turning on the "also check for beta versions" in PopChar Preferences -> Updates, such that you will be informed as soon as we have released the beta.