Facebook team always busy for new updates that may result pages owner to face some issues for the time being. Also you face some issue that make you surprise similar like the schedule post. Publishing post have three different options, learn publishing and schedule here.
Recently when I tried to schedule a post on a page but there was no schedule post option instead there was only Backdate and Save option. I found the solution in the business version of the page and page doesn’t need to have a business admin inside the role.
Simple goto business version by adding “business.” before facebook.com e.g
https://business.facebook.com/scienceinventions/ now you can easily schedule unlimited posts.
You can also manages post from Creator studios too.