If I'm keeping my current iPhone, do I need to backup and restore?

You won’t lose any data from switching carriers. If you are changing your phone number you will have to disable, then reactivate Messages and FaceTime, and also change the phone number for 2 factor authentication. For 2FA add the new phone number as a “trusted Number” BEFORE making the switch.

When you restore a backup made previously everything will be restored and your phone will have the same settings, apps, contacts, etc that it had before. But unless something goes wrong when you switch you won’t have to restore the backup.

Having nothing to do with your carrier choice, you should be backing up regularly to be prepared for disasters, such as your phone being lost or stolen, dropped in a toilet, thrown under a bus, or just failing. Unless there is nothing on the phone that is important to you and that you wouldn’t miss if you no longer had access to it. As you can set it to automatically back up every night it isn’t even really an inconvenience→How to back up your iPhone, iPad, and iPod touch - Apple Support

It never hurts to back up. It may well hurt not to back up.

Could have that IPhone backed up and kept somewhere safe as a backup in case something happens to your current iPhone