I have the same issue (app crash) just after MacOs has updated the companion app to version 2023.12. If I restore the app to previous version (2023.7) using time machine the app works fine… I assume it is something related to the new 2023.12 version. (I have MacOs Catalina 10.15.7 on an iMac 27 - end of 2012)
Just an update: You can download Testflight and download their Test Flight build. The issue seems to be Apple’s implementation of Matter/Thread in OS 13. This should fix the issue until HA releases a fix.
Another update:
I am running on MacOS 12.7.2. Companion App 2023.12.1 runs just fine.
Today the Appstore advertised an Update of the App. (2024.1) I installed it and it immediately crashes when I try to start it.
Fortunately I had a TM Backup from before, so I restored the app.