Just picked up my Shark and I’m trying to track down the factory winch handle + jack tools. Can’t seem to find them in the tub or under the seats — are they usually supplied loose,

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Hahah looks like it's standard practise

Behind the rear seat. Download the manual from the BYD website, they show how to retrieve the jack and use it.

The grey case was there but no tools inside it

take it back to the dealer!

None of them do. Our friends bought a brand new Lexus EV and for +$100k it didn't come with one either. I ordered a spare tyre kit separately for our SL6 that I take on trips out of town.