The System administrator or the application administrator are unable to select the custom scoped application from the application picker.
Application administration is checked for the custom scoped application in the sys_app table. As part of the administration, customer might have created application admin and application developer roles. For these roles, the elevated privilege option might be selected as per the below screenshot.
If Elevated privilege is selected, the user should either elevate their access upon login or they should uncheck the Elevated privilege option so that the access will be granted without elevating.