I agree. I think the issue is she maybe feels a bit exposed. And the lollystick ladder does look a bit like a magnet for injuries unfortunately. If she climbs she will think it's a way out and if she can't get out she will jump.
They do need somewhere dark to retreat to. I would also pop a big house in there - eg a shoe box makes a good size and she can build a big cosy nest inside it (it's cold weather at the moment so they need a big cosy nest) and have space to bury her hoards and even put a litter tray inside it with chinchilla sand in - she will either use it as a toilet or use it for something else! So cut the base out of a shoebox and keep the lid as a lift off roof. Sit it on top of the substrate (maybe right side?). I would take the climbing lolly stick thing out and put the house there. Then cut a hole for a door in one of the long sides near one end (it means the other end is darker inside). Putting the litter tray at the back at the door end usually works as they seem to nest at the darker end. If you put a bendy bridge over the door that makes it dark inside and it'll tempt her to move in (tunnel entrances tempt them in). Put a smelly treat inside the house also to tempt her in - eg a bit of cucumber. The lid/roof makes something to climb onto that isn't too high and is safe and you could put a food bowl on it eg.
Then a big pile of nesting material nearby (but not inside the house - let her forage for it). Torn up strips of plain white toilet paper are best as they're safe to use and they like it for nesting.
I would hold fire cleaning her out a bit longer. Although it's a month,it's agood sized cage with plenty of substrate, and she does sound stressed at the moment. If you think it's too smelly then I'd suggest getting her out in a playpen area or a pet carrier, and just cleaning one half of the cage substrate for now. Keep back some of the old substrate that is clean and not too whiffy and spread that on top of any new substrate you put in the half that you clean. Assume you know not to use any scented cleaners? They can be overpowering for a hamster and affect them. Maybe the right half where there is less substrate, and add a bit more at the same time. Then the other half will still smell familiar and she'll be less stressed by the change. And add the house at the same time on the clean right half - the treat should tempt her to explore it. I think she'll approve of that change, although generally they don't like things changing,but they do like new additions that help them have normal behaviours (the large house will mimic a burrow with space for nesting, hoarding and peeing). You could even have the house part subterranean - ie push it down into the substrate so only the top 2" or 3" is showing. You can "channel out" a bit of substrate down to the entrance door. With a lift off roof also you won't need to take the house out - you can just take the roof off to spot clean inside in future and if it gets messed up it's just cardboard and can be replaced.
She may also need more to do in there and with a large cage they need to feel secure and have plenty of "overhead cover" - things to dive under or sit under. I would add a platform and a few floor tubes/tunnels - kitchen roll inner tubes are good and larger ones are good too (eg pringles tubes). Rather than popsicle sticks, something that is solid is better.
A few people have used this one - it's probably as cheap as buying the bits and pieces to make one. It's quite tall (21cm) so would be better either at the end where the substrate is deep (so you don't need too high a ramp to get up to it) or next to the house- where you could have a low ramp from the house roof to get up to it eg. eg another bendy bridge on the house roof where it'll be more stable.
https://www.amazon.co.uk/Trixie-Natu...V0CBE41K9757JK
Another option for a house, if you don't mind buying one - is this - hamsters seem to love labyrinth houses as they're dark inside and it has two entrances- always nice to see their head popping out of the top hole
It is open underneath as well but one section near the entrance has a bit of floor in it which most people pull off (supposed to be quite easy to pull off) so it doesn't get pee soaked if an accident occurs in that part. Always check wood houses for protruding nails as well -but I haven't heard of any issues with this one. It also has a lift off roof.
https://www.amazon.co.uk/Trixie-6201...V0CBE41K9757JK
Your hammy's stressy behaviour does suggest something isn't right with the cage environment or some other stress and she probably just needs more enrichment and things to sit under and be in the dark sometimes.
I also think though that the dog being nearby could be causing some stress as well. Although it may seem they are friends, just the smell of a dog or cat can create great fear and stress in a hamster, with hamsters being prey animals. It would be better if you could keep the dog away from the hamster cage.
Final question - what kind of ventilation is there? Assume it's on top? They do need good ventilation especially in an enclosed tank style cage like that. Ideally the top would be full mesh.