Hi, Averly, Gray, budgies and tiel (no names?!). Welcome to the forum and thank you for taking in a bird that needed a home -even if it's only temporary.
Now, to be perfectly honest with you, I do not do anything with my birds but, then, I have a number of them and, in one way or another, they all interact with each other. Plus, they fly - which is pretty much all they need to do to keep occupied. I do have a few that don't and what I do is exercise their wings so that's something that you can do with her every day (even twice a day). It will benefit her immensely from a physical point of view and it will mean something else to do. I make them step to my hand or a stick and lifting it as high as my arm will allow, I bring it down suddenly and fast so the bird, feeling it's 'falling', will flap its wings. I do this over and over for a few minutes at a time and, if I have time, I do it more than once during the day. Now, a bird that did not learn how to fly as a baby will never, ever be a good flier but the exercise strengthens the muscles, stretches out the shrunken tendons and allows the posterior air sacs to inflate and deflate properly (which prevents infection). And, if the bird still retains a little bit of flight, it helps them increase it. I have a bird that never flew (he only glided down to the floor) and is now able to maintain horizontal flight for a good 8 and, sometimes, even 10 ft.
In my personal experience (I've cared for 6 grays), grays mostly like to be included in our activities. My Sophie Gray (the only one I have now) likes to 'supervise' from my shoulder. She looks attentively everything I do and, if there is an activity that calls her attention, she takes part in it - for example, she loves to watch me brush my teeth and after a few seconds of making sure I am doing it right, she grabs the end of the brush with her beak which moves her head up and down, back and forth until I finish - and, if I let her, she would eat the toothpaste, too
Then there is always foraging. A piece of birdybread (don't ever feed a parrot human bread or any other cereal product meant for humans) wrapped in paper and put inside a box she needs to open (you can even get one with a simple lock she would need to open before the lid of the box) to get to it. Or put inside a little cup (like the ones they sell for mouth wash:
https://www.amazon.com/Disposable-Bever ... NrPXRydWU=) cover with a piece of paper that you will tie around the rim with a twine (you can put a large grape in it, they love grapes). Start by putting the stuff inside, covering the cup and tying it in front of her so she can see what's inside and teach her to open it by herself - once she learns, you can get a number of them done in advance and just give them to her all at once.
I am not one to recommend teaching parrots useless tricks but grays are highly intelligent and will benefit from extra 'thinking' activities so you can get some baby activity toys for her, too (like putting colored rings around pegs, for example - or the kind that the baby needs to turn pieces like these:
https://www.amazon.com/Spunky-Kinder-Wo ... 60&sr=8-12https://www.amazon.com/Fisher-Price-Sta ... 60&sr=8-26They also love things that make noise and she might like getting a little baby piano or xylophone that she can bang on with her beak.
But, as I stated before, in my personal experience, all they want is to ride your shoulder and check on everything you do - especially if it is a physical activity like sweeping, mopping, dusting, etc. because 'their thing' is to belong and to be a part of everything their human does.