Are sub-Neptunes rocky cores with hydrogen or water worlds?

In plain words

A planet two or three times Earth's size can be a rocky ball with a thin hydrogen layer or a world with a large fraction of water, and mass and radius alone cannot tell which. Their atmospheres carry clues.

Precise statement

For planets with $R \sim 2-3.5\,R_{\mathrm{earth}}$ and $M \sim 5-15\,M_{\mathrm{earth}}$, determine the bulk composition: rocky cores with H/He envelopes of $\sim 1-3\%$ by mass, water mass fractions of $\sim 10-50\%$ in supercritical layers, or magma oceans that dissolve and mix with hydrogen. The answer is a classification of individual planets and the population fractions, using JWST transmission spectra (mean molecular weight, $\mathrm{H_2O}$, $\mathrm{CH_4}$, $\mathrm{CO_2}$, $\mathrm{NH_3}$ abundances) together with interior models.

What would settle it

High signal-to-noise transmission and emission spectra of a sample of temperate and warm sub-Neptunes fitted with coupled interior-atmosphere models.

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