Neither one can fulfil the other’s orders
Two marketplaces, and no fulfilment relationship between them. That is their rule, not a gap in ours.
People connecting a shop to a marketplace often expect the marketplace to ship for them. This pair is two marketplaces, so there is nothing to arrange in that direction. eBay cannot be told to fulfil a TikTok Shop order, and TikTok Shop cannot be told to fulfil an eBay one. Neither platform offers it to the other, which means picking and posting stays with you whichever side the sale came from.
What is left is the part that matters anyway: one stock figure across both. Items match by SKU, and a sale on either marketplace lowers the other, so you are not trying to keep two sets of listings honest by hand. That is the whole job on this pair, and it is worth being clear that it is the whole job rather than implying more.
Being two marketplaces has one practical consequence beyond fulfilment. Neither side is the natural home for your catalogue, so decisions about naming and structure belong in the middle rather than on the platform you happen to prefer. If you have been treating one of them as the master copy and the other as a mirror, this is the point to stop doing that.