on my new iphone 13 i cannot use face id to open my locked notes

Touch and Face ID may not be able to unlock a note after our iPhone has been restarted, restored, or updated. You need to use the password that you entered when creating the notes. Once you do that, you will be able to access them with Face ID again.

https://support.apple.com/guide/iphone/lock-notes-iphf177bb154/ios

blair1945 Said:

"on my new iphone 13 i cannot use face id to open my locked notes"

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For Troubleshooting Tips, Visit these Links:

• If Face ID isn't Working on your iPhone or iPad Pro - Apple Support

• If you can’t Turn on or Sign in to iMessage or FaceTime - Apple Support

• If you can't Make a FaceTime Call on your iPhone, iPad, or iPod touch - Apple Support

• If an Alert Says Face ID has been Disabled on your iPhone or iPad Pro - Apple Support

• If you Experience an Error when Trying to Activate iMessage or FaceTime - Apple Support

What does his problem have to do with FaceTime and iMessage? Did you read the link that edclange provided?