Callers can access apps and other info on iPhone 13 Pro

You’re triggering Face ID. Cover the Face ID camera temporarily and test again to verify this.

Could not reproduce this behavior.

(the incoming call can be answered; but no additional access to ANY of the device’s other functions are allowed)

Are you sure that it’s not simply the FaceID authenticating the authorized user?

If you feel an unauthorized person/app is remotely using, controlling or monitoring your device, then that is possible only if you have done one or more of the following Don'ts...

1. Don't hand over an iPhone to kids or to a stranger without Enabling Guided Access
2. Don't share Apple IDs
3. Don't Jailbreak
4. Don't share sensitive information pertaining to your device
5. Don't give in to Phishing
6. Don't plug in your device in Airports and Public places through third-party cables and trust the device. Beware of Juice Jacking. (Especially in India)
7. Don't leave your iPhone unlocked and unattended in public places like offices, schools, malls, etc.

If one of the above is true then quickly change the Apple ID Password and Return iPhone settings to their defaults.