First things to check are - is the water bottle working? Is the wheel spinning/working? Sometimes bar chewing is to frantically tell you something really important.
Otherwise can you show a photo of your cage set up? That can make a big difference as to whether they are happy and settled in it. A small wheel or something else not right in the cage can lead to bar chewing (as in "I want to escape!").
The other common cause of stress leading to bar chewing is cleaning out too often and too much. Weekly cleanouts aren't necessary and full clean outs aren't recommended.
If you've just done a full cage clean that could be it. Better to do "partial" cleans - less often. The way to do this is - you need enough substrate in the cage - fill the base to 1cm or so below the rim of the base. Add a litter tray with Chinchilla sand in - syrians will use one if you put it in their chosen pee place.
Then you just empty the litter tray every few days. You can "spot clean" the substrate when needed by taking out a handful and adding a new handful and mixing it in. With a litter tray it can stay clean and dry for a very long time with spot cleaning.
When you do come to change the substrate, keep back some of the old clean substrate and spread it on top of the new so it still smells familiar (that top layer will gradually get spot cleaned out). You actually use less substrate this way as well even though it's a lot to start with. But don't clean anything else at the same time as doing the substrate. Do the wheel a different week and any other items a different week again. Leave the nest and hoard unless pee'd in. They are very precious about their nest and hoard and if those are regularly thrown away that can lead to bar chewing stress as they don't feel safe.
Another thing that can stress them after a clean is anything scented - best to just use warm soapy water on the cage base and rinse well. Pet disinfectant isn't needed unless there's been illness or disease. They have a very sensitive sense of smell and respiratory tract so anything scented can affect them badly.
Cage set up is another thing - if something isn't easily accessible - eg food or water. Or a ramp that collapses on them or is wobbly. They also need somewhere dark to retreat to so a house that's big enough to build a big nest and dark inside goes down well. If you're using the Hamster Heaven as it comes then there isn't a good house in it. The little plastic ones get stinky inside and need cleaning out too often. Also the supplied wheel is too small and they can get back pain so stop using it (then they get pent up energy and bar chew). The penthouse and tubes also lead to abnormal behaviours like peeing and nesting in the tubes and needing them cleaned out too much.
So a good option with that cage is to get rid of most of the plastic stuff and add a good house/nesting box and a 28cm wheel. My suggestion would be to leave the solid shelf in and remove the other one, take out the tubes and penthouse and block off the tubes (the cage comes with tube blockers) and add a 28cm wheel and a house like this. It's not cheap but very good and works well.
https://www.rodipet.co.uk/houses/rod...t-rodents.html
A cheaper option is this which is a good size and also has a lift off roof but really needs a bendy stick bridge over the door to make it dark inside
https://www.ferplast.com/gb/sin-4645.html
Cheapest option is a shoebox house - cut the base out of a shoebox and use the lid as a lift off roof. Cut a hole for a door on one of the long sides near one end (the other end is then darker). Again putting a bendy bridge over the door makes a nice tunnel entrance and makes it darker inside.
Anyway basically see if some adjustments will help your hamster settle.
I have the same cage but with smaller bar spacing - set up like this. It's identical to the Hamster Heaven and exactly the same size but without the tubes and penthouse and narrow bar spacing (Savic Mickey 2XL). Rat sized tubes and houses work better for syrians.
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