Axe-Edit is a separate piece of software and does not get updated automatically when a new Axe-Fx II firmware is released. The Axe-Edit developers have to manually add any new features that come from the Axe-Fx II. So if a new parameter or feature is added in the latest Axe-Fx II firmware, there is usually a new version of Axe-Edit to be downloaded and installed. On average it takes a few days to a few weeks for the new version of Axe-Edit to be available.
This is especially true of any Beta or Public Beta firmware releases; Beta firmware are usually tests, and the new features may be completely changed or taken away, so it makes sense for the Axe-Edit developers to wait until features are confirmed and officially released.
Generally speaking, most current/older features that worked in Axe-Edit will continue to work even with the new Axe-Fx II firmware and the older version of Axe-Edit. However, there are exceptions, and major differences or incompatibilities are usually mentioned in the Axe-Fx II Release Notes (RTFRN).
If you heavily rely on Axe-Edit, it is suggested that you do not update the Axe-Fx II firmware until an updated Axe-Edit is released.
It seems that the current philosophy is to release Axe-Fx II firmware with new features as soon as possible, rather than hold back its release to wait for Axe-Edit and/or other products to become fully compatible. This philosophy seems to be supported by majority of users. As mentioned many times on the forum, it is NOT necessary to update to the latest Axe-Fx firmware as soon as it is released. If you need Axe-Edit, it is advised to wait. If you are in a recording session or touring, etc. it is advised to wait. It is advised to only update firmware or software versions when you have time to test and troubleshoot.