Welcome, uwpe90!
From your post, it sounds like you are experiencing an issue with the Calendar invitations that you’ve received. We’re glad that you reached out to the Apple Support Communities and want to try and help you get this resolved.
Are these invitations received in Calendar, a calendar notification or in Mail? Also, are you able to send invites to contacts and receive a notification that they have accepted or declined? If you’re not sure, please test it out for us.
Also, check for any macOS updates: Update macOS on Mac
Try booting into safe mode, logging in and testing to see if the issue persists. You can find the steps for safe mode located here: How to use safe mode on your Mac
If you’re still noticing issues after safe mode, check to see if this is something that's isolated to just your user on your Mac, or if it's system-wide. Please use the steps from the section “Add a user” to create a new user on your Mac: Set up users, guests, and groups on Mac
Have a fantastic rest of your day!