How is the SI unit for mass defined (as of 2019)?

Question

So, the SI unit of mass is defined by taking an exact value for Planck's constant, which is units of J$\cdot$s = kg m$^2$ s$^{-1}$, and meter and second already defined in ways I understand. I don't understand what physically fixes the value of Planck's constant.

Planck's constant gives the proportionality between the frequency of a photon and its energy. The frequency is in units of inverse time which make sense, but I don't understand what fixes the energy scale on the other side of that equation. Is it something like $E=h\nu=mc^2$? Is there some other usage of Planck's constant that is defining its value? Joule is not one of the SI base units and is defined in terms of mass.

How is the value of mass defined, i.e. of what physical system is the fixed value of Planck's constant representative?

Edit: it looks like the answer is it's a parameter that shows up in many equations and thus can be found by various experiments, e.g. Bloch oscillations in rubidium. Is this true, or the standard experiment? It is surprising to me that this isn't as fixed and straightforward as the cesium definition of a second.

Does this answer your question? What are the proposed realizations in the New SI for the kilogram, ampere, kelvin and mole? — Michael Seifert, Jan 29 '23 at 17:48
Not exactly, but it is helpful! I see the statement: "Note that macroscopic masses can be measured in terms of ℎ, using the Josephson and quantum-Hall effects together with the watt balance apparatus, or in terms of the mass of a silicon atom, which is accurately known in terms of ℎ using the x-ray crystal density approach." and later that h can be derived from Bloch oscillations? So there's a few different ways to determine h? — qmstatmech, Jan 29 '23 at 18:38
Also related: https://physics.stackexchange.com/q/342947/123208 & https://physics.stackexchange.com/q/477485/123208 — PM 2Ring, Jan 29 '23 at 19:54

How is the SI unit for mass defined (as of 2019)?

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