After a bit of a peruse of Digikey, it looks like I might have a match!

I took some measurements (0.4mm pitch etc) and made a few assumptions as to brands, I assumed that Sony would use a Japanese brand for their Japanese product, so looked primarily at Hirose and Panasonic offerings (I didn't preclude other brands, though, just in case).

It turns out that Panasonic parts AXK740147G‎ (for the socket) and AXK840145WG‎  (for the plug) are looking preeettyyy close to what I'm after.

https://www.digikey.com/product-detail/en/AXK740147G/255-2534-1-ND/1986697/?itemSeq=291802877
https://www.digikey.com/product-detail/en/AXK840145WG/255-2527-1-ND/1986690/?itemSeq=291802878

Next step, add these parts to an order and see if the plug fits the socket on the motherboard.