New Rescue

Poor girl. Honestly, as scared as she is, I would just be giving her space. Try to avoid things that might come off as scary to her, like staring or coaxing. Even trying to tempt her with treats might be too high-pressure until she gets a chance to calm down. Spend time in the same room as her, but well out of her space and do something non-threatening like reading a book instead of paying attention to her. For meals, I'd honestly just feed her on the couch (maybe with a towel under the bowl). Let her eat at her own pace and try again not to hover or stare. I'd avoid picking her up at all, if you 100% have to move her, have her wearing a collar and a light house line and use that to gently encourage her to move (assuming you can get a collar and line on her safely).

She's very, very scared from your description. Any attempts - no matter how kind or positive - to urge her to move are probably going to stress her more until she's able to relax enough to take in her surroundings and realize things aren't dangerous on her own. If you find she isn't improving at all over the next couple weeks, I would urge you to talk with your vet about anxiety medications. The purpose of these is to get the fear under control so the dog can actually learn that you and the world isn't scary, and how to act like a normal dog. She may only need it temporarily, or it may benefit her long-term, but either way it's a very good option for a dog this fearful if she isn't coming around on her own.

Look into the 2 week shut down for shelter dogs. It's keeping them near the center of things but crated or penned so they don't need to be handled and cannot make any mistakes. I happen to have an exercise pen and put water, a bed and a toy in there. Every hour I take the dog out on a slip lead to potty. I use a small treat inside the loop of the slip lead so no grabbing for the leash loop on a collar and pop the dog back in the pen with another treat.

In your new dog's case I'd do the same. Put the bowl of food in with her at meal times. If she eats right away that would be amazing and just take it away when she's done eating. If not then leave it for a good long time at first. This would probably be very like the way she was treated at the puppy mill but baby steps.

My first dog and newest dog both didn't eat well when they came home. Sassy was so out of it she couldn't figure out when it was meal time for close to a week and Bucky would only eat treats for the first 3 days. It's not good but definitely not way off the bell curve.