Page = procedure?

Yes, but more broadly, "borrowing a page from" means using a technique that someone else has had success with. You might "borrow a page from" the playbook of a successful coach in sports for example.

You must look at the entire idiom:

"Borrowing a page" from modern manufacturing . . .

It means "referring back to how it's done in modern manufacturing"

You may also see: borrowing a line.

Borrowing a line from a famous person, it ain't over till the fat lady sings.

In UK English an old fashioned word for a page in a book is "leaf" - you still see this in words like "overleaf" which means "on the other side of this page or piece of paper". A "loose-leaf" file or folder is one where the pages are not tightly bound, e.g. a Filofax.

If we are copying somebody's method or procedure or attitude we might say that we are "taking a leaf out of his book".

Thank you all.