How do I put an iPhone 13 in recovery mode

See these instructions:

If you see a iPhone, iPad, or Apple Vision Pro unavailable message or Security Lockout screen - Apple Support

If your ex didn't properly prepare the iPhone to be given a way, it's possible that it is still locked to his Apple ID. If so, you won't be able to finish activating the phone until it has been removed from his account.

See here:

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Follow the instructions from this link 🔗

If you forgot your iPhone passcode, use your Mac or PC to reset it - Apple Support (CA)