Are there SMD variants of the JST VH 3.96mm connector series?
As far as I can tell from the JST website, JST does not sell any SMD variants of the JST XH series.
However, LCSC lists some 3rd party SMD connectors as VH 3.96mm, such as:
So far I have not tested those and I don’t know yet if they are compatible with the standard JST housings.