I'm having the exact same issue on my Note 20 Ultra. On the Samsung Members app, there is a duplicate banner ( the black friday deals one ) presumably where the One UI 4 Beta registration should be. I've reinstalled it, restarted the phone multiple times etc. After researching on the topic I'm only finding reports/info about the beta from the UK. I really have no idea what's going on.
Edit: After looking some more it looks like Samsung removes the registration banner after some time because of a user registration limit. This is just based on other posts so I'll wait for any official notices.
P.S I was also wondering when my phone's contract ends will I be able to unlock it or at the very least will the phone functions like an unlocked phone so I can join betas in the future?
Nope. That's the problem. I have an AT&T phone that I paid off and got unlocked. It still doesn't have a U1 model number so it won't get the beta.