Some females do need a lot of space. If she has been used to a barred cage as well she may be having difficulty adjusting to the tank style. They always try to look for a way out and the top is the way out! It's very common for them to chew the water bottle hole as well.
It's a good sized cage but I think that style is a bit limiting on what you can do for enrichment as it's not particularly tall or easy to fit shelves in. There are some good 100cm barred cages that are a bit higher (but not too high) allowing for shelving as well as good depth of substrate and a lot more variety. I'll add a photo of our recent Savic Plaza set up - it's still 100cm x 50cm like your cage but has a lot more scope.
On the other hand you may worry she would bar chew in a larger barred cage. The only real alternative then is something like a detolf or 4 foot fish tank, both of which are good options for Syrians.
The detolf is an ikea hack. A cheap option for a glass tank as tanks are really expensive. It's a glass cabinet tipped on its side with the door left off so it's open at the top. It then needs a lid (usually two smaller lids) makign so a bit of diy involved - just some strips of wood with mesh attached though.
You can find some reasonably priced second hand 4 foot fish tanks (I could never find one) but again they would need a lid making.
These are difficult decisions as they involve cost!
If she's been in the (is it a Zoozone?) for 3 months now and not settling it does sound like she might need a bit of an upgrade to a different style of cage. The advantage of the Savic Plaza is the interaction with the hamster as well as it has a large front opening door. And they seem to like that. Ours come to the door when you open it and put the paws on and go nose to nose for a bit
Also as Ria says, if her wheel isn't big enough that could make her hyperactive. The 28cm trixie wheel should fit if it's the 100cm zoozone. And yes if there's a shelf she will climb on it and try and get to the top bars. So something with a bit more height would be helpful there.
It may just be needing more enrichment and more to do in the cage. Have you got a photo of the set up?