Would it be bad if I threw away the backpack that my ex had me purchase online for her?
Do you really want to throw away her backpack?
Yes, but I wanted to get her this special one because she seemed to like it.
Even though the relationship ended, it is not good to keep antagonizing an ex by throwing away her things. She could report you for throwing away her things.
She said that I'm a bad person and that she deserved so much much more. There is a 99% chance she will never contact me again anyways.
Throwing away your ex's backpack is wrong, unless she made it clear that she does not want it. If that is the case, you should donate it.