What about something like this?
I dunno what the arrangement of your stairs is like, but this is what mine is like and reflects what I've been wanting to do ever since I moved in here.
The problem with mine is I've a step-up to the threshold, and then a step-down beyond it - which kinda scuppers the use of anything on castors.
You could screw a couple of battens inboard of the castors to the floor under the stairs, to ensure the trolley doesn't crash into the sides.
Frequently required stuff is on the front edges of the wall-mounted shelves on the right.
Less frequently required stuff on the trolley.
Archived stuffs on the in depth wall mounted shelves.
Mine comes as close to that as poss - with the exception that all the stuff where I've shown the trolley, has to be hand-balled in or out.