Well, Tesla isn't really treating it as a trade secret, they told their numbers to CA DMV back in March, but didn't ask them to withhold it as a trade secret. Elon has also publicly said they have ~2000 testers now. Elon's previous goal was expansion to ~10k, that's my guess for the next target with the button release. I don't feel like it'll be a wide release.
But anyways, it matches my impression of what the button means: it's a replacement for the emails, and Tesla will still be vetting people before approving them. Some people thought it'll straight up download it for use, no questions asked, but it's pretty clear that's not what's going to happen.
FSD Beta Videos (and questions for FSD Beta drivers)