On my Galaxy Note 20 Ultra 5G the on-screen thumbprint seems to be finicky.
Occasionally it takes more than 1 scan because I didn't angle my thumbprint directly perpendicular to the phone screen.
Make the thumbprint reader a visible rectangular box that you need to place your thumb somewhere within the designated area.
A couple of tips I picked up when setting up the finger prints are @Kyle_T
When setting up take x3 scans with each thumb and then rotate the phone around when taking further prints of each thumb so your phone can read both thumbs from the same finger print scan. Scan your prints as you would normally hold the phone.
Also using two fingers when setting up one fingerprint works pretty well.
Go into Settings . Biometrics and Security. Biometrics Preferences . Turn Off Screen Transition Effect.
Then go into Settings and search for Optomise Battery Usage. Tap in Optimise Battey Usage tap to show All and scroll down to com.samsung.android.biom and toggle Off
For me this improved the fps on my Note.
I also have dry skin on my fingers and so find it sometimes beneficial to moisten my fingertip by breathing on it before unlocking the phone.
Current Phone ~
Samsung Note 20 Ultra 5G SM-N9860_256Gb SnapDragon 865+
Samsung One Ui 3.1/ Android 11.