I try to configure teams call pickup group with 5 members. The idea ist to ring (signal) the call first for 10 seconds by the original recipient (callee) and after 10 seconds to ring all the call group members simultaneously and after another 20 seconds to forward the call to an auto attendant. When simultaneously ringing ist set for the call group the call gets signaled immediately by all the group members and the 10 seconds wait time is gone.
Can you check the 5 members of the Call Group all the members are enabled for Enterprise Voice. That could be one of the reason why it is not working.
Alternatively you can configure a Call Queue in the Teams Admin Center and add all the users from the group to the Call Queue and then on the regular user can forward the call the DID of the Call Queue and from Call Queue it can overflow to AA.