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You could try having a little water bowl as well. He probably is drinking - they don't drink that much so you don't see the bottle going down really. The main thing is that he can reach the water bottle - then he'll work it out when he's thirsty.
A bowl needs to be small so they can't fall in it - getting wet isn't good for them. I use these one of these little Ikea glasig tea-lights and have it in the corner of a shelf, where it can't be knocked over.
Ikea Glasig - click here
They do tend to live mostly at ground/lower level as they like to dig and burrow and even make tunnels and burrows. So having a lot of substrate at ground level will really help. It might also lessen the angle of the ladder so he's more likely to go up it

It's usually recommended to have about 8" deep of bedding, but 6" minimum. He'll like that. Could you move the house to the ground level as well? As they usually like to bury their hoards under the nest where they sleep. So it helps if a house is on top of the substrate and open underneath. If the house is a bit small they sometimes don't use it and nest under a shelf instead. As well as substrate, if you give him a big pile of torn up strips of toilet paper, then he'll use it to make a nest - if you haven't already that is!
He's still a baby

It's nice he lets you pet him. Is the ladder solid or is it rungs? If it has rungs with gaps, that might be why he's not going up it. They can't really manage ladders like that. But if it is, you can adapt it by glueing a piece of thick cardboard or wood to the back - then it's like a solid surface with rungs
