How to prevent additional user from sharing SMS?

I have a Google Pixel 4A 5G phone running Android 13. I added an additional user with System -> Multiple Users and enabled calls and SMS for the user. I am surprised that my messages are shared with the user. The documentation states that messages and apps are not shared. I chatted with Google Support but the person wasn't helpful. How do I prevent my messages from being shared with the additional user? See https://support.google.com/pixelphone/answer/2865944?hl=en which states the following: