Could you first try to uninstall dv-runtime, dv-processing and libcaer via Homebrew, and then check that the normal DV.app you download from our website works?
If yes, reinstall the above via Homebrew and try running 'dv-runtime --version' first from command-line and then 'dv-runtime' with no arguments, what's the output?
We only test and build on MacOS Monterey 12.X, so make sure to have an updated version, and if you want to build from Homebrew, also an up-to-date XCode and Homebrew itself.
Hope this helps a bit, have a good day!