How do you get out of SOS only mode on an iPhone 13?

Because you don't have Service.

See -> If you see No Service or Searching on your iPhone or iPad

If you see No Service, Searching, or SOS on your iPhone or iPad - Apple Support

Charge also the battery > 70%.

See -> If you see No Service or Searching on your iPhone or iPad

If you see No Service, Searching, or SOS on your iPhone or iPad - Apple Support

This page has some information on what SOS only means on iPhone.

You have to contact your carrier and have them add your phone to a mobile service plan.

Click the hyperlink in my post and read it.

The call your carrier and tell them to fix your account. SOS means that you have a cellular network connection, but it is not on a valid plan.