The full release it estimated for October if your device is eligible for the beta you'll see a banner on the main page or alternatively you can press the bell icon and the invite should be in the notices tab only unbranded devices are eligible for the beta
Joined the Beta program this morning & currently pulling down the release - not that I'm expecting great leaps, doing it more for research purposes. I've a factory unlocked S22+.
If your device is eligible then there will be a banner on this (Samsung Members) with an invite to opt in. To be eligible then your handset needs to be UK factory unlocked; ie. Not from or supplied by a network provider.