Op it sounds horrific. But as this clearly isn't just a work issue for this person, you are going to have to be very clear about boundaries in your shared space.
Both of you have to have an equal amount of storage space to arrange as you see fit. Be it filing cabinets, shelving. It doesn't matter. A tape line down the middle of the desk/shelving is an excellent idea because you both get to organise your personal space within that defined boundary. They can have everything everywhere if that helps them work. You can have yours tidied away if that works. But both need to adhere to whatever clear desk policy/shared information resources your company lays out.
However, I would not be pushing things back into their space. If it encroaches onto your space, you reserve the right to deal with it in line with company policy, ie file/scan/bin.
By all means keeping scrap paper is good, as it saves money and resources. I used to use it instead of endless post it's for taking phone messages as long as there was nothing confidential on the other side.
Is it possible to have a small shredder in your shared office to keep on top of hoarding?
But your manager also needs to manage this person effectively.
Pamphlets which are out of date they should be insisting go.
If you do have a clear desk policy, for cleaners etc. Then your manager needs to use whatever performance and development scheme you use to record that it's not being done and make it a target to achieve.
But if their house is as bad, it sounds like they need more professional help than work can give them sadly.