Hi Staphanie,
Thanks for writing to us.
For push notification badges increment, you need to extend your message by badge increment as show below:
PushNotificationService pushNotificationService = App42API.BuildPushNotificationService (); // Initializing PushNotification Service.
string userName = "UserName";
string message= "{'message':'Hello! I am here','badge':'increment'}";
pushNotificationService.SendPushMessageToUser(userName,message, new UnityCallBack())
Kindly find the link which will contain the full details that how you can integrate the push notification badge process in your app.
Let me know if it helps.
Thanks.