TIL they operate their own DTC sites (of course). Will give those a try next time.
~2016 I worked for an Amazon Marketplace seller – avoiding the banhammer was our biggest priority, having been banned once because a unisex fragrance (perfume) we sold "smelled too masculine" and therefore the customer told Amazon it was counterfeit.
Given we often had inventory available in FBA (Fulfillment by Amazon) and not in our own warehouse, we often fulfilled eBay orders via FBA.
I've been out of the business for awhile, I think the rules around this from eBay's end have changed. Regardless, it's common for sellers to use 3PL (third-party warehousing and fulfillment) services, FBA or otherwise.