I’m very glad that I stumbled across this thread as I’m experiencing the same issue with both our existing theme (not a 2.0 theme) and also a popular 2.0 theme that we are currently preparing and setting up for future use.
I found the new Transfer UI quite frustrating (losing the ability to scroll through transfer search results using the arrows that were in the top right of the page is very annoying) and I assumed that perhaps our existing theme was no longer able to display the ‘variant.next_incoming_date’ due to this term having been updated.
However, as has been pointed out, ‘variant.next_incoming_date’ is still shown in the dev reference.
Even when updating one of our theme Sections, Shopify’s own auto-complete feature still offers the ‘variant.next_incoming_date’ as a suggestion, and I can’t see an option for anything similar using slightly different terminology.
I have also checked the very popular 2.0 theme that we are currently working on and this also makes reference to ‘variant.next_incoming_date’ on both the product and cart pages. All usage of ‘variant.next_incoming_date’ appears not to be working and is returning not returning any information, so I can only assume that Shopify have perhaps updated this terminology (maybe to something along the lines of “Estimated arrival” as shown on the transfer UI) and haven’t made the information publicly available, which isn’t particularly helpful!