Just to confirm that budgies unfortunately will refuse foods they don't like/aren't used to...
One of my young birds made herself sick from not eating enough while I was trying to convert her and her cagemate to a healthier diet. The ONLY things she would eat were sprouted seeds, offered in small portions, dry millet, and dry canary grass seed from the mix they were, and still are, on. I would blow out the hulls to find that she (and he...) still hadn't eaten other types of leftover seed, pellets, or the dried fruit in the mix. So, I would put it back in the cage. They wouldn't touch much of it, and I'm betting that he was the one taking all of whatever was eaten. I'd top up the bowl, and put it back. She started puffing up after a couple of days, acting lethargic. An increase in her food, and she got better, and much more playful with her buddy! Even accepted regurgitated food from him. Hopefully he's eating well enough that it passes on to her. I've given them cat grass and veggies, but he's the only one who bothers to nibble. Next thing to try is dicing veggies/fruits, and mixing it in with the seed mix. Hopefully she'll get to liking the taste.
I'm sorry for your losses, and excited for your new bird! Do make sure to check the items in your home for things that may be coated with teflon, etc, just in case. Best of luck from my birds and I!