Products are either their own record with their own data in the products table ...

or, they are Linked Products that share 1 record ...

If you copy a Product as a Linked Product, then everything about the Product is shared ... quantity, price, etc.

If you copy a Product as a Duplicate Product ... you have made 2 Products and each of the 2 Products has its own price, quantity etc. and there is no relationship between the 2 Products ...

This means, that you cannot have the same Product with 1 price in 1 category and 1 price in another category and share the quantity as they are 2 separate Products when you do a Copy as Duplicate Product ...