I need to identify what spyware has been installed on my iPhone 13

See -> Delete suspicious content from your devices

Delete suspicious content from your devices – Apple Support (UK)

To keep your Apple ID account secure, see the following Apple articles: 

If you think your Apple ID has been compromised

If you think your Apple ID has been compromised - Apple Support

See who has access to your device or accounts

See who has access to your iPhone or iPad – Apple Support (UK)

Check your Apple ID device list to see where you're signed in

Check your Apple ID device list to find where you're signed in - Apple Support

• if you see devices that don't belong to you, delete from your account.

Personal Safety User Guide

Personal Safety User Guide – Apple Support (UK)

Manage and use your Apple ID

Manage and use your Apple ID – Apple Support (UK)

(if you haven't already done this) Two-factor authentication for Apple ID -> Two-factor authentication for Apple ID - Apple Support

Change your Apple ID password -> Change your Apple ID password - Apple Support (IE)

• Create a strong password for your Apple ID, It is best if your password consists of eight or more characters and include upper and lowercase letters, and at least one number. You can also add extra characters and punctuation marks to make your password even stronger. 
• Never provide your password, passcode, security questions, verification codes, recovery key or any other account security details to anyone else. Apple will never ask you for this information.

Then see this Apple article: What to do after you change your Apple ID or password

What to do after you change your Apple ID or password - Apple Support

Never jailbroken your iPhone.

Unless you gave the phone to someone for an hour or so while it was unlocked there is no spyware on your phone.

And if this did happen just restore it to factory settings and do not restore a backup→Restore your iOS device to factory settings - Apple Support