Apple Lightning to USB cable - do I need to buy a USB adapter for this cable?

It fits into the 18W USB-C power adapter that is shipped with the iPad Pro's. You can also just use any other USB-A to lightning adapter you may have for your phone to charge the AirPods pro case.

Apple is heavily pushing the use of USB-C, that may be the reason why they included that type of cable with the Pro's

They do but I don't think it's what you need since it has a male USB-C plug:

https://www.apple.com/shop/product/MJ1M2AM/A/usb-c-to-usb-adapter?afid=p238%7CseF44721a-dc_mtid_1870765e38482_pcrid_246386725857_pgrid_14874603490_&cid=aos-us-kwgo-pla-btb--slid---product-MJ1M2AM/A

I was simply answering the question of the OP which was if Apple sells a USB-C to USB adapter. I prefaced the link with my doubt that it would work since it has a male USB-C plug. I don't see where confusion can occur if the entire answer is read.

you can use a USBA to lightning connector the same one you would use on an iPhone.

If you look on the apple website it explains what cables come with the device

That adaptor wouldn't work

That's what I said

Why link something that doesnt work?

Its adding confusion for no reason

You would be far better off spending your money either on Apple's 18watt charger with USB-C or buying a Qi wireless charger.