Not sure what the Software Update Center is, but you would download it the same as any OTA update on your device.
Settings | Software Update | Download and install
It does take a few minutes from the time you enroll, until the time it shows up. If this is what you are trying, just wait a few minutes, and try again.
Did this confirm your enrollment? What happens when you go into the Members app now, is the beta banner still at the top? If the banner is there, try enrolling again, and watch for any messages, such as the beta being full. You may have overlooked this last time, and did not actually get enrolled..
Strange, I signed up then went to check and it was there. I'm not sure how it's doing with others but up to now it's been really stable on my S22 Ultra. The only issue I've had on occasion has be Secure wifi would close but it never interfered with my connection.
