How do magma oceans change sub-Neptune atmospheres?

In plain words

Under a thick hydrogen layer, the rocky surface of a sub-Neptune may be molten, and hydrogen can dissolve into it and react with the rock to make water and other gases. This would change what the planet's atmosphere looks like from outside.

Precise statement

For sub-Neptunes with surface magma oceans at $T \sim 2000-4000\,\mathrm{K}$ under $\mathrm{H_2}$ envelopes of $\sim 1-3\,\mathrm{percent}$ of the planet mass, determine how $\mathrm{H_2}$ dissolution into silicate melt and reactions with the melt (FeO and $\mathrm{SiO_2}$ reduction producing $\mathrm{H_2O}$, SiO and $\mathrm{SiH_4}$) set the envelope composition and its mean molecular weight $\mu$. The answer is predicted $\mu$ and $\mathrm{H_2O}$, $\mathrm{CO_2}$ and SiO abundances versus equilibrium temperature and envelope mass fraction, testable against JWST spectra.

What would settle it

Coupled magma-atmosphere equilibrium and evolution models that predict the dependence of $\mu$ on equilibrium temperature, confirmed by JWST spectra of a sample of sub-Neptunes spanning that temperature range.

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