I have tried two different screen protectors on the note 20 ultra and the fingerprint sensor does not working at all. I regret switching to this phone from Apple. Apple face recognition works so well. I can not even register a fingerprint with a screen protector and will not use a phone without one. Hating this switch.
I'm using a Ringke Dual Easy Wing screen protector and the fingerprint sensor works fine.
Did you register your prints before putting the protector on or after? You usually need to register them after it has been placed on.
What you need is a screen protector with adhesive on the entire screen. The ones with adhesive around the edges alone will create a gap between the screen protector and the screen itself, thus causing the fingerprint scanner to either not work, or have degraded performance. As for using this as the sole purpose of locking your phone, I do not recommend it. Use a password, a PIN, or a Pattern, all other methods can have law enforcement officers, or criminals, force you to unlock your device.
Same issue with my Note 20 ultra. I've tried three screen protectors but fingerprint scanning is still hit and miss (mostly the latter). My prior phones - Note 9 and an LG - - worked much better for this function (and considerably less expensive).