If you don't have it on the main page on members app your phone maybe not eligible.
For s23 the phone needed to be directly from samsung and have the September security update.
If you do have it press on it and press again on the picture and enroll at the bottom. After 10 min check for software update few people said had to wait longer. Just make sure you read the disclaimer.
It seems it's for Samsung phones bought directly from Samsung and not ee or O2 etc. Iv never had the beta appear on my members app ans iv had Sammy phones from day1. Best getting a pixel if you want to get the betas. They offer it from day 1 and it's so straight forward. And reliable, quick and easy to go back as well... There's so many hurdles when phones have skins and then on top of that phone providers have to check and test etc. Hence the long delays if it even comes at all. And even when it does it's released in small batches. Tbh just go with pixel like I say if it's quick access you want.