Are you sure that all of these birthday events are generated from your Contacts app? Might some be from a manual entry in your Calendar app?
When I activate the Birthday calendar using the Calendars > Other options I see a grey birthday parcel icon. I do not use this automated calendar and prefer instead to enter the birthday events for family and friends manually.
For my manually added birthday full-day events I also see an icon which might be confused as a parcel (or birthday present) icon but it is in fact the new square calendar icon and bears to colour of the calendar to which I have added it in my Calendar app.
These calendar apps to the left of an all-day event are a new feature added to the Calendar app and were introduced in iOS 18 and macOS 15.