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This is all assumption from me, but I think a lot of testing would likely be diagnostic machines and specialized testing -- not actually playing games. I would assume it's something like plugging in, confirming the parts all meet spec after whatever the refurb is. That spec is probably more around frequencies, power use, temperatures.
Obviously that's not good enough if they're sending out these clearly broken refurbs.
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.