I am sure many of you are aware of the miniaturizations of MH lamps. Commonly available down to 20W and 15W, with prototypes being made down to 3w or maybe even lower (I think I remember seeing a 2w one here but I can't remember).

Recently while browsing Trad Lighting, I came across this post from Max detailing a 15W SON lamp, designed for use with 20W fluorescent chokes. This is very interesting, as I haven't ever heard of HPS below 35W before. As far as I am aware this is the smallest HPS lamp ever made, though feel free to prove me wrong, I would love to hear about it.

That leaves MV behind. The smallest MV lamp I have seen is the North American 40W H45 lamp whish isn't even that small. I would assume that any attempts to miniaturize it would be for scientific/microscopy applications rather than general lighting due to the poor efficiency. Has anyone heard of MV lamps under 40W? Any experimental designs?

I don't think there was ever any motivation to make such small MV lamp.
The 50W were already a challenge - very high temperature to keep the arc voltage high enough with just a short electrode gap in order to maintain somewhat reasonable arc loading, not enough power to maintain that temperature already at the 50W (needed vacuum outer, special heat reflective coating on arctube end seals,...), so rather high cost offering barely any efficacy benefit. You may be able to get something from skipping the starting probe, so allowing to make the seal assembly smaller and dissipating less heat, but then you would need some HV ignitor.
With lower power that would become way worse, so much that a simpler long life incandescent would perform nearly the same (efficacy, lifetime), with the way better light quality as a benefit, all at fraction of the cost.

The HPS was at least seriously considered because of the efficacy benefit, still did not make it till high volume production.

MH made it because the efficacy and light quality (thanks to the CMH), allowing them to compete with halogens for the high end display spotlight market where the high purchase price was offset by the lower energy consumption (because it uses to run 16+ hours/day) and way lower heat generation (giving more flexibility to the display arrangement).
Well, someone considers MH as an evolution of MV (it uses similar buffer gas, evaporated mercury, just with some additives), so by that metrics these small MHs are in fact those "small MV's"...

I think it is definitely possible to make, see all these modern SHP mercurys, but why do one needs such a lamp? Purpose?

MH chemistry works better, and anyway square/cube law works against smallish lamps.

By the way, my 50W Osrams do not have any heat sparing coatings on the arctube, just a hard vacuum outer bulb.