The NLRA says "Nothing herein shall prohibit any individual employed as a supervisor from becoming or remaining a member of a labor organization, but no employer subject to this Act [subchapter] shall be compelled to deem individuals defined herein as supervisors as employees for the purpose of any law, either national or local, relating to collective bargaining."

...which effectively states that if a supervisor joins a union it's a no-op. The employer is not required to acknowledge their membership. In practice, unions specifically exclude managers for a bunch of obvious reasons related to their ability to bargain effectively on behalf of their members.

Your manager likely joined a union-ish entity open to supervisors. IIUC such entities are not protected by the NLRA and as such have few of the legal powers and protections that make a union a union. They’re basically affinity groups.