I accidentally deleted a favorite game which is not in my App Store cause it’s so old. How do I get it back??

Does the app show in your purchases in the App Store App? From the App Store start page, tap your avatar in the upper right corner. In the resulting window tap "Purchased:"

then "My Purchases."

Scroll through the list to see if your old app is still listed.

Sometimes I've been able to restore old apps that way.

I found a thread with a similar situation. There’s a long shot in there but unless you have an old computer with an old version of iTunes that might have the app file there’s not much hope I’m afraid

Moving a Discontinued App from Old iPad t… - Apple Community

I am sorry but you may not be able to get it back.

To the best of my knowledge, apps are no longer backed up locally so if they’re gone from the App Store, they’re gone.