I bought my wife a refurbished 512GB unit as soon as I heard they were available. It was delivered about a week later on a Thursday and immediately, we noticed battery life was very poor compared to mine.
Desktop mode showed battery health at 17%, and so by that Saturday, it was packed up to be sent back. Ended up going with a new unit instead, so your story sounds a lot like ours, sadly.
Yes, that’s exactly what we did - I’ve been happy with my new unit since January, and when her refurbished one was a dud, she said, “Let’s just get a refund and buy me a new one.”
I, as well, had applied a screen protector right off the bat, but I’m glad I didn’t put the skin I’d bought her on it before we noticed it wasn’t in good health. Thankfully, it was painless and cost-free to return it, but I agree - if they wasted some of your time doing the testing they themselves should have done, it would have been nice to get some kind of compensation as a token of apology.