Does the 2022 Apple 10.9-inch iPad (Wi-Fi, 64GB) support face ID?

No.

Touch ID ONLY

Apple Pencil 1st gen ONLY.

All models of iPad in recent years support either TouchID or FaceID - but not both. The iPad9 supports TouchID.

All iPad models that support TouchID have a physical Home Button at bottom centre of the screen - within which is the TouchID sensor - or for iPad Air4 and mini6, incorporate the TouchID sensor within the Top (Sleep/Wake) button.

iPad models that support FaceID have a FaceID sensor (consisting of an Infrared Dot Projector and TrueDepth Camera array) - this sensor being absent from iPad models that support TouchID.