Upon installing and going through the setup process for iPadOS 13 Beta it didn't allow me to set up the device using Face ID also this is the case once the device is set up it refuses to activate the cam and just errors.
Face ID Issue
FWIW, FaceID that was previously setup under iOS 12 was preserved for me upon upgrade to iPadOS 13.0 (beta).
So is yours a new iPad or did you do a factory reset before installing the beta?