Calendar invite acceptances across devices

I'm using OS X Calendar with my Gmail account and my employer's Exchange system. If I receive a calendar invite, it shows up on all of my devices — my Mac, iPhone and iPad. But if I accept or decline it on one device, that is not reflected on the other devices, and I have to go through the same routine of accepting or declining it. It couldn't be iCloud, because the events themselves are syncing. Running Sonoma 14.6.1 on my Mac, and right up to date on my iOS devices. Not a big deal, but one of my settings must be wrong.