Does anyone have any suggestions on what I should do in this situation?
He texted at one point that I should throw out his stuff - he doesn’t need it.
I believe he answered your question on what to do with his stuff, throw it out.
And it does sound like you care more about his “stuff” then he does. It’s been months that you’ve been broken up, he came and got the one thing he really wanted and left the rest for you to deal with. Throw it out so that you can fully move on in life. Holding onto his stuff, the stuff he really doesn’t care about might be a way you are still trying to hold onto him.