iPhone shuts down at 20% battery despite being fully charged

But the battery is at 100%

It might say that it is at 100%, but it is not at 100%. You have a defective / failed battery and its real condition is not being displayed correctly.

If you want to keep the phone, make an appointment at the Apple Store / Genius Bar or take the phone in to an authorized Apple service shop to have the battery replaced. About $90 (U.S.)

You can find a list of authorized Apple service shops in your area using this link:

Find Locations

Those are classic indications of an iPhone battery nearing the end of it’s useful life.

If it’s the original battery in your upper-middle-aged phone, it’s almost certainly the case.

Battery health <80% is a sure indication if this is indeed the case.

Check the iPhone battery health and usage - Apple Support

If you decide to continue using that phone into the future (it will NOT receive any more major iOS updates):

iPhone Battery Replacement - Apple Support