She might have been abused. @FrayedBear had a good suggestion with the glove. It may take her longer to trust you or learn how to play gently. Good luck and keep us updated please.

Tough call. I would suggest clipping her sharp claws to minimise injury to yourselves for a start. Then Have you tried wearing a thick leather gardening glove to protect yourself then simply hold it out to her after she has fed? Let her attack but offer no retaliation. Eventually she will realise you will not. If she is play boxing still with the glove on play box her paws back allowing her to get some punches in. Laugh whilst doing it.
When my old girl and I were much younger we used to have some roughhousing on the top of the bed. I would roll her over letting her spring up and swipe at me and yes sometimes I'd forget to blunt her claws and end up with bleeding scratches. She would simply be rolled off, tummy or chin tickled so that she was distracted from fight mood. Sadly now that she is old and i think getting a little demented and to say nothing of my skin becoming thinner, I have to be a lot more careful and we only cuddle not roughhouse.
I don't know if this will help you at all. It may just be a matter of her establishing herself in a new home. I would not pursue what i have suggested for too many weeks. If no change occurs i would suggest the more drastic aversion therapy of using the water spray bottle to spray water on her every time she scratches.

How does her companion cat react to these outbursts? Is the other cat scared or asleep or disapproving or competing for attention ? Are there dogs or cats outside your home ? Do you have a harness to walk her outside ? Does she have windows to see outside ? Do you have many toys to burn off steam in play ? Let her chew on a catnip filled fake mouse and maybe chase one of those red laser lights. ...keep her busy and avoid her swipes & bites. ...my cat Laila gives me gentle love bites for more or different food or just more shoulder massage. ...besides the ear rubs & jaw tickles. ....You live with another human so both of you need to be on the same page keep a journal and see what treats she likes. ...vary wet & dry feedings. ...she is like an acrobatic toddler human with tiny vocabulary. ...be a good parent and let her teach you her ways

How old is she? It sounds like she has a strong play drive and you need to get some feather flyers and play with her until she tires out.
At least twice a day.

If they don't get enough play time they'll play "Hunt the human".