Since March, Google has been maintaining two active channels of beta updates for its smartphone users. The Pixel Feature Drops are now part of the Quarterly Platform Release (QPR) branch, while the upcoming major Android revision has got its own track. In accordance with the new strategy, the company delivered Android 12 QPR3 Beta 2 and Android 13 Beta 1 in April. The current state of the Android beta program feels like a hot mess, as Google has now come up with a set of temporary restrictions for beta enrollment for the month of May.
Earlier today, Google published a short post to the /r/android_beta subreddit, detailing what Pixel owners opting in for the beta initiative can expect after the Android 12 May 2022 stable release. The post states that if you've already installed the May security patch on your Pixel device, you should be able to enroll in the beta program, but the beta OTA will be delayed. This is because both the latest available Android 12 QPR3 Beta 2 build and the Android 13 Beta 1 build are older than May's update. As a result, one must wipe their device to perform the transition.
Fortunately, the waiting period for the QPR branch is rather small. Android 12 QPR3 Beta 3 is "coming this week," according to Google. Those who want to switch to the Android 13 Beta branch need to wait a bit longer, though. There is no concrete timeline for the Beta 2 release ("coming soon" is the exact verbatim of Google). Moreover, even after installing the QPR3 Beta 3 build (once available), you will not immediately receive Android 13 Beta 1 and will have to wait until the arrival of the Beta 2 build.
Keep in mind that the restrictions are only applicable to the over-the-air beta update mechanism. If you are no stranger to manual flashing, you can easily switch between the beta update tracks on your own. However, it's worth mentioning that the flashing process completely wipes the target device, thus it is highly recommended that you back up your data before proceeding.
Source: Android Beta Program on Reddit