Shopping/wish list should be transient until saving with some products. A collection of lists should be stored in store theme settings. Be sure that personal cabinet should not create a persistent lists.
There is another issue. To reproduce it just create a new customer on storefront, after that go to product page and click "Add to list" button. Storefront API will return 400.
Shopping/wish list should be transient until saving with some products. A collection of lists should be stored in store theme settings. Be sure that personal cabinet should not create a persistent lists.