I wouldn't switch the toys just yet. It sounds more like stress after moving to her new cage. She hasn't been in it that long has she? They need a good couple of weeks to settle in - so if you've maybe changed anything recently or done a clean that might make her want to get out!
There are also good hamster chews you can get - I like the Rosewood naturals ones but they're not easily available except online. The Vitakraft ones are easily available. I stopped using those as they have honey in so not good for their teeth! But in the short term it would be a good treat and would distract her demolishing it.
If it's stress and you change things around now it could make her more stressed. Starting bathtub taming is a good idea. If you can try and do it around the same time each time she'll know she'll be coming out at some point (ie a bit of a routine) and that might help reduce the bar chewing too.
Other reasons they do it is if something is a problem in the cage - eg empty water bottle, wheel stuck or wedged and not working etc.
Apart from scatter feeding a bit, adding a new chew or a new toy or some extra substrate, I would leave everything in the cage untouched for another week or so while she's still settling in.
I have a little video on taming our Syrian in the bathtub, if it helps
We used to let him either climb into his ball - by holding it just inside the cage or near the door, and transport him up to the bathtub in the ball. Sometimes we'd use a tube - putting one end of the tube in the cage and the other end in the ball as he didn't like hands in the cage at first. So he'd walk into the tube and into the ball that way. Then gently put the ball down in the bath and take the lid off. When he'd had enough he used to jump back into the ball. If you put a dry towel on the bottom of the bath it gives a bit of padding. And a few toys (cardboard tube or any kind of hidey place like a mug on its side).
https://www.youtube.com/watch?v=kjyEme2xcq4