My iPhone is stuck on SOS mode, is it hacked?

See more of an explanation here:

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

It’s not locked to any carrier

That may be true, but the real question here is.......who is your cellular carrier?

If you are saying that you don't have a current carrier, then SOS will continue to be displayed until you set up service with a carrier of your choice.

If you do have a carrier set up, you need to contact them and ask them to troubleshoot the network connection to your phone. When you have cellular service on your phone working again with the carrier, the SOS notice will be gone.

That just means you have no service. Contact your carrier to ensure you have service with your iPhone.

Best of luck!

NOTHING in that linked support article even mentioned “locked to any carrier” ???

Suggest that you might consider a re-read.