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Let's start with a few questions. Since this is the first time I'm looking into this I would like to gather some information and see if we can troubleshoot our way through this.
What device do you have? Not that I believe the device has anything to do with this but because it will help me navigate you through some of the menus if I know the device.
Was this recently? I ask because if you have notification history turned on I would like to gather some information from the notification if possible. I will assume for the moment that you have access to your notification history, it should be easier to access, but the easiest way I've found is to open Settings and type history into the search bar you find there. Notification history should be one of the choices. My notification history goes back a little but seems to end at just over 24 hours. Touch the notification and see if it says what account the information is from, and basically anything and everything the notification says. I would even touch the notification to get it to open the associated app and see if that gives us any additional information.
You mentioned looking in some apps for this contact but let's look in them all, starting with your Google apps. If you're like me you may use other apps to access your Google information, for instance, I use Samsung Calendar to enter reminders and appointments, but also receive notifications from my attached Google account. I would like you to go to Google.com in a browser and sign in to your account. Next to your profile picture there are 9 dots, touch those and navigate to calendar. Use whichever view is better for you and go to the date of this former contact's birthday and see if it appears here. If it does you can edit from this view in any way you like. Next, whether it appeared or not, let us also check your contacts. Again, this is one where you may not be using or editing the correct contact source. Using those same 9 dots, open Contacts. Use the search bar at the top of this view to search for this former contact.
If searching your Google data did not turn up any leads as to where this notification is coming from, let's do the same to your access apps. You likely have two calendar and two contact apps in your app drawer, let's open the non-Google ones and repeat the search for this former contact and event date. While in your alternative contact app, you should find that somewhere along the top, usually, there is a drop down which will show you options for accounts to pull from. You may have to open a side menu or a dropdown of some kind, I believe by default most will likely say All Accounts, but if you touch this it will show you the individual accounts information is pulled from. For instance in my list I have, Phone, Google (main Gmail account), Google (side Google account). I years past I also had some other provider accounts listed here so it can be other accounts besides Google. And next to each there is usually a number indicating how many instances are stored there. By touching one of the alternative lists, navigating away from All Contacts, you can then search each of the ones you have listed to see if this former contact appears in any of those lists.
Let us know what you find and we'll go from there.
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