USB 3.2 to 3.0 adaptor

That would depend on whether you ever want to plug a USB 2.0 device in or not. I can't see any reason not to connect it.

Anyway, the adapter you linked appears to do the reverse of what you want. It connects a Gen 1 case connector to a Gen 2 motherboard port.

My base model X570 Elite had both kinds of header.
 
The Akasa AK-CBUB51-BK should do what you want. I'm sure similar adapters will be available elsewhere.

What X570 motherboard do you have that doesn't have the header you need? Or do you need more of them than are available?
 
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