Fingerprint button not working as designed

The iPad User Guide describes the straightforward process of setting-up TouchID:

Set up Touch ID on iPad - Apple Support

If you are having difficulty setting-up TouchID, refer to this support page:

If Touch ID isn't working on your iPhone or iPad - Apple Support

As documented by Apple in its Security Guide, for devices with TouchID or FaceID enabled, you device Passcode will still be required in the following circumstances…

A passcode or password is also required if the device is in any of the following states:

• The device has just been turned on or restarted

• The user has logged out of their Mac account (or hasn’t yet logged in).

• The user hasn’t unlocked their device for more than 48 hours.

• The user hasn’t used their passcode or password to unlock their device for 156 hours (six and a half days), and the user hasn’t used a biometric to unlock their device in

4 hours.

• The device has received a remote lock command

• The user exited power off / Emergency SOS by pressing and holding either volume button and the Sleep/Wake button simultaneously for 2 seconds and then pressing Cancel.

• There were five unsuccessful biometric match attempts (though for usability, the device might offer entering a passcode or password instead of using biometrics after a smaller number of failures).

When Face ID with a mask is enabled on an iPhone, it’s available for the next 6.5 hours after one of the following user actions:

• Successful Face ID match attempt (with or without a mask)

• Device passcode validation

• Device unlock with Apple Watch

Any of these actions extends the period by an additional 6.5 hours when performed.