Mobile applications can behave differently based on the design and limitations in their corresponding mobile operating system.
The reason for GlobalProtect App prompting the user for user name and password is because of the authentication profile (e.g. using RADIUS or LDAP services) selected in Gateway configuration.
Authentication protocols like RADIUS and LDAP often require username/password combination. The GlobalProtect app would fetch the information from the user to be presented to the authentication server at the backend. This behavior is by design.
Even in some rare scenario where authentication server at the backend does not require both user name and password, The end-user experience could also be different using PC (Windows/Mac OS) because, with single sign-on capability, GlobalProtect would forward username/password combination to Firewall for backend authentication without prompting user's input.
Enable " Save User Credentials " in client authentication settings under GlobalProtect Portal GUI: Network > GlobalProtect > Portals> (portal name) > Agent > (agent name) > Authentication. So user only needs to enter their username/password combination one time.