Can I copy only Contacts to new phone

I don't think there is a way to do a selective restore of a backup.

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

You might be able to export all of the contacts from your old phone to iCloud, then import the contacts from there on your new phone.

Import, export, or print contacts on iCloud.com - Apple Support

Then you should make sure your contacts are synced to the cloud, restore your phone back to your factory settings and once you sign in your apple id after that, contacts will sync back to the device.

Set up iCloud for Contacts on all your devices - Apple Support (CA)

You can also download from the Apple Store a Contacts app, there are many, you can save your contacts in a file that can be transferred to another iPhone, but the quickest way is to sync contacts from the iCloud