> What is it about Stradivari or other hand made instruments that make them so coveted, are desirable sonic characteristics measurable and traceable to manufacturing techniques? Or is it all just halo effect?

It 90% halo effect.

However, the wood, in particular, for the Stradivarii came from forests that had suffered droughts and was quite a bit denser than expected for that species.

That having been said, wood degrades. It doesn't matter if you put magic varnish on it or not. Wood ages nicely in instruments for about 10 years. Then it's good for about 50 years. After 50 it starts noticably degrading, and the more heavily used the more it degrades.

You will note that the Strads are long past the point that the wood is "good". People who play violins can tell. However, nobody involved in a "blind" test is going to slag violins that might be Strads--that would be bad for their reputation.

Ironically, those Strads aren't completely original, either. They have been repaired to various degrees over the years, given more modern bridges, etc. So, we get a Ship of Theseus argument.

As for modern handmade violins, the top ones are easily as good or even better than Strads. Strads may have been "magic" in the 1700s and 1800s, but we have really good control of things, better measurement, better analysis, better materials, etc. in the modern era.

Luthierie in the 2000s is still art, but it's got a lot of science backing it up nowadays.