@cmillerLCE @Nino Bilic
Ok, this Add-In issue is a weird one. I noticed that one user "Chuck" on an updated server (Test environment) was affected, another user was not. Btw, I did not apply the workaround for the EWS crashes as I didn't see the error messages in Application Event Logs.
So checked the Organization Apps (Add-Ins) and found only one additional Add-In that was provided to the affected user. I removed the assignment to Chuck (Set-App -UserList ...) and voila, Add-In management started working again for Chuck. I then reassigned the Add-In to Chuck and now he can manage his Add-Ins again and the Add-In seems to be working at a first glance. I wasn't expecting this. Not sure what to make of this behaviour.