Lastest LRc feature down arrow on previews wants you 'save' what?

The way that Lightroom Classic and Photoshop are intended to work together (*), whether or not you save editing metadata to the starting Raw file on disk is completely irrelevant.

Consider: when you are editing a virtual copy to PS there is no possibility of writing edits to the file, and this makes no practical difference whatever.

SO far as what comes back into LrC from PS: the Catalog does know about this because it was the Catalog which commissioned its creation. This consists of a physically separate file (a TIFF or a PSD) and only the contents of that are referred to. There is no further dependence on the originally edited Raw by this new image version - let alone, on any editing metadata written - or not written - alongside that.

All the same comments apply when you start from (say) a camera JPG rather than a Raw.

(*) 

It would be possible to instead start up PS directly, browse to the relevant Raw using that, Open into ACR. If you had previously made edits to this Raw using a LrC Catalog and then written out those edits to file, ACR would see and use those. Just the same as if you had previously used ACR and it had written out edits. OTOH if you had previously made edits in a Catalog or in ACR but then not written those out, there would be none there for ACR to see.

And when you edit further within PS and save the results to a new TIFF or PSD: Lightroom Classic will know nothing about this either. The whole sequence would be simply none of  the Catalog's business.