Does factory reset via iTunes erase eSIM during iOS update?

Restore your iPhone, iPad or iPod to factory settings using a computer - Apple Support (IN)

Resetting an iPhone to Factory settings using Finder/iTunes doesn't delete your eSIM. Find out how to erase your eSIM, if you need to erase it.

When you factory reset an iPhone, you are presented with the options to either keep or delete the existing eSIM settings.

If you do not want to lose the eSIM settings on the phone, you would choose the option to keep the settings on the phone.

If it is a dead phone, you will not be able to do anything with the iPhone until it is repaired.

The repair shop will Factory Reset the phone for you. Ask them to keep the eSIM configuration, if possible.