It’ll be some cmake work. The first step would be to compile using -DQT_VERSION=6 along the lines of this pull request: Add a build matrix for Qt 6.5 by ghutchis · Pull Request #1282 · OpenChemistry/avogadrolibs · GitHub
IIRC, the problem is that there’s no support for Qt6 in generating the deploy script.
The avogadroapp CMake files need to add in qt_generate_deploy_app_script | Qt Core 6.6.0 which should take care of many things.