Based on the following I understand that new custom fields of an existing custom object aren't available to users after Pushing a Managed Packaged
From the link one option it recommends to allow users access to new custom fields in a Managed Package is to create a new Permission Set which has access to the custom fields. Then create a Post Install script that assigns users to the new Permission Set. The users assigned to the new Permission Set should be those who have access to the component of the custom fields.
I created the new Permission Set and Post Install Script and it assign users to the Permission Set who have access to the Object of the new Custom Fields
I tested this is our Business Org and it worked! When I deployed to a customer who has our Managed Package installed, the Permission Set was created in their Org but no one was assigned to it; not even Admins.
Any idea why the users who have access to the Custom Object didn't get assigned to the new Permission Set?