The work sounds interesting, but the article is painfully written.
Lead acid batteries produce hydrogen too. I think the insight is that this can’t produce electricity directly, so the chemistry can be much more stable.
The paper, linked below (thanks xelxebar) would beg to differ, it says
> we report a rechargeable manganese–hydrogen battery, where the cathode is cycled between soluble Mn2+ and solid MnO2 with a two-electron reaction, and the anode is cycled between H2 gas and H2O through well-known catalytic reactions of hydrogen evolution and oxidation.
They give an equation for the cell operation as,
Mn2+ + 2H2O ↔ MnO2 + 2H+ + H2
Mn2^+^ + 2H_2_O ↔ MnO_2_ + 2H^+^ + H_2_
> During discharge of the battery, the uniform layer of as-deposited MnO2 on the cathode is dissolved back to soluble Mn2+ electrolyte and H2 is oxidized on the anode.
So, I guess it stays in solution...?
Mn₂⁺ + 2H₂O ⇌ MnO₂ + 2H⁺ + H₂
(Shameless plug: I generated the above with https://github.com/jwilk/chemiscripts .)
https://doi.org/10.1038/s41560-018-0147-7
which redirects to the Nature Energy page and so is behind a paywall. I'm not sure how Sci-Hub is viewed here, but this links directly to the pdf:
This is very much NOT explained by the paragraph,
> The researchers did this by re-attaching their power source to the depleted prototype, this time with the goal of inducing the manganese dioxide particles clinging to the electrode to combine with water, replenishing the manganese sulfate salt. Once this salt was restored, incoming electrons became surplus, and excess power could bubble off as hydrogen gas, in a process that can be repeated again and again and again.