Calendar invites to my apple id mail do not go to the calendar app, only to mail

Any calendar invite sent to my iCloud mail, which is also my apple id mail, goes to mail, despite having the setting that all invites should go to the calendar app. It happens on my MacBook Air (2 years old), my iPhone 16 with the latest iOs (was the same on my now dead iPhone 13) and it's the same in iCloud.

It works with any other calendar on any other mail account, but NOT on the iCloud mail.

Does this work for any of you, with an iCloud account?