I agree with Riven that you probably will need to upgrade her cage, female Syrians especially do need quite a bit of space.
If she’s nervous does she have nough cover in her cage to help her feel safe & secure? She needs a good size house, about the size of a shoe box, with no base on deep bedding so she can burrow down. Also extra hides in the cage to there isn’t too much open space, if the cage is too empty it can make them feel exposed & vulnerable.
Also for taming I personally think the bath tub can be a bit intimidating for a hemser, can you set up a play area in the same room as her cage so scents & surroundings are more familiar.
As well as changes to or upgrading the cage you can do things like scatter feeding rather than just using a bowl so she can forage for food which is more natural & will help to distract her from bar chewing. You can also make things out of cardboard to hide treats in or stick seeds to, have a look at this thread for some ideas.
This is a thread to show how many things you can make for your hamster or enclosure, out of cardboard :-) Cardboard is your friend.
www.thehamsterforum.com
I wouldn’t give greenies they aren’t really good for them & whimzees are a much better option.
You can use things like dandelion root or apple wood which may be more likely to interest her than just wood or loofah chews. You can also get sprays of millet & flax (linseed) which they enjoy striping.
She is still young & everything is still new for her so give her time to settle & give her more things to do in the cage for now.