Not only would the cat stress the hamster, but more importantly long-term is that these “Critter Trail”-style enclosures are not big enough for hamsters. At all. Full stop. Maybe for a weekend if the hamster is over and you can’t bring the full thing, but especially for what looks like a Syrian(?), this is a solitary confinement cell, not a living space.
For background before I get into specifics: hamsters’ entire lot in life is that they love to run long distances, explore, and burrow. When they spend hours running on their wheel at night, it isn’t because they’re bored; it’s because that’s naturally what they do, but in a vast, open wilderness.
It’s widely accepted among the hamster care community that the barest bare minimum floor space is 450 square inches. And this is often below what veterinary organizations recommend. It seems pushy and elitist, but in reality – similar to goldfish in aquariums – the pet industry are greedy fucks who want to do everything they can to lower the barrier of entry for hamster ownership, so they market hamsters as Tommy’s first pet that he can keep on his night table. 450 is arguably a compromise just so it isn’t as daunting to hamster owners who didn’t know before and want to do the right thing. Moreover, the recommendation for Syrians specifically is 600. (The 450 figure applies to dwarf hamsters as well; they’re just as ridiculously hyperactive.)
For context, these “Critter Trail”-style enclosures are often maybe 150 sq in, or about 1/3 of that (1/4 for Syrians, which I think this one is). Hamsters have to have room to run around and explore. It isn’t a nice-to-have; for them not to is, without any hyperbole, animal abuse. Additionally, they need to be able to burrow. It seems like that isn’t possible in this enclosure, but hamsters really need that to feel secure and not constantly stressed. By “burrow”, I mean several inches of bedding (ideally throughout, but if you’re in a pinch, one corner can be the burrow mound). The combination of needed floorspace and the fact bedding needs to be stacked high for burrowing pushes a lot of hamster owners to get a glass aquarium on a good sale and use that as the enclosure (it works super well). Some also use plastic tubs, but this has a DIY aspect to make sure your hamster has enough air.
If this hamster has to live in the enclosure pictured for the rest of their life, they’ll be nothing but chronically stressed – quite probably even fated to die early from it. This isn’t meant to be preachy; it’s just a reality that hamster cage companies are lying to you to make you feel better.
EDIT: Wheel is also – unfortunately – comically small for a Syrian. Syrian wheels are much larger, and wheels this small can permanently injure them. If anyone reading this specific part doubts this, I want you to look back at the picture and, in your mind’s eye, try to put that hamster on that wheel without bending it into an elbow macaroni.
>Be me
>Placed by aliens in a tiny cell with no hiding spot
>Suddenly there’s a wolf spider with a 20-meter legspan outside staring me in the face
>My mind goes blank as I realize I would be torn limb from limb but for the flimsy bars of my cell walls
>“Quit assuming the human is afraid. The spider is probably friendly. You’re just projecting, bro.”