The forum over
https://community.developer.atlassian.com/t/welcome-to-the-early-access-program-for-atlassian-s-new-navigation/85219/6
seems to be dead so I'm posting this here as well.
I found a bug/breaking change regarding our apps Better PDF Exporter and Better Excel Exporter. In team-managed projects, users should be able to export from the Board screen but in the new navigation, the meatball menu for the “jira.software.board.tools” entry point only appears for admins.
In this screenshot, the user on the left is an admin, while the user on the right is not. The meatball menu appears for the admin (from where they can initiate an export with either the red “Export PDF” or the green “Export Excel” option) but it doesn’t appear for a regular user.

However, if I switch back to the old navigation with both users, the apps’ entry points appear at the top of the board for both users and they can export.

As I see it, Zephyr Squad is also affected.