If you recently updated your iPhone to iOS 17.7 or iOS 18, it is normal for the battery to work really hard for several days after the update to reindex all of the data on the phone. Battery Health might drop 2-4% after a major update.
The serial number of the Apple charger does not tell us if the product is real or not. You will need to take the charger to an Apple Store or authorized Apple service shop to let them check and test the charger if you are concerned that it might be a fake.
Since the charger was working normally before, it is highly unlikely that it is a fake.