There is no longer an android 12 beat as it went official about 2 days ago, final release, previous flagships never get the beta, so you needed an S21, and next year you'll probably need an S22 to get in the beta.
Yes the beta is over, but the s20 did receive a beta program this year, the same as with one ui 3 where both the s20 and s10 got the beta. So next year will be s21 and s22
I have the Samsung s20 ultra as well and I signed up for the private beta for Android 12 start of November and been using it since, maybe you missed the sign up
