Yes your phone model should receive the new software.
More information in > https://www.sammobile.com/news/samsung-devices-eligible-for-upcoming-android-13-update.
In regards to the Beta Programme the best place to check is your Samsung Members App. If it becomes available in a region for an eligible phone model then the invitation would appear there.
As for the release of the full version after Beta Testing then the release date / month will become evident later down the line once Beta testing has concluded @Rizzla
Daily Driver > Samsung Galaxy s²² Ultra 256Gb in Phantom Black.
The advice I offer is my own and does not represent Samsung’s position.
I'm here to help. " This is the way. "