For the record, I propose as a possible explanation, albeit, involving a more advanced depiction of the underlying chemistry, to account for why with zinc sulfate electrolysis leading to zinc metal, there is an apparent absence of significant hydrogen gas evolution.
The answer starts from the excellent presentation given by Martin on this very forum (see "Electrolysis of Water" ) as to likely mechanics involved therein.
In particular, note the cited formation of surface radicals including formation of atomic hydrogen, or, as also referred to as the hydrogen radical, in the realm of chemistry of radicals. Normally, this step is immediately followed by hydrogen radical self-reaction liberating hydrogen gas. So for most purposes, the omission of this step is not usually problematic.
However, in the special case of zinc, and I would also reference aluminum metal, there can be a significant surface attachment of the hydrogen radical. In essence, we have now further wandered into the field of surface chemistry for which I refer the reader to a 2008 doctoral thesis by Saikat Adhikari, "Alkaline dissolution of aluminum: surface chemistry and subsurface interfacial phenomena".
So, bottom line and quite simply, I suggest there is some possible surface chemistry intervention occurring with water electrolysis in the presence of zinc metal (long noted as a powerful reducing agent with association to 'nascent hydrogen'), such that one could witness a reduction/cessation in the apparent evolution of hydrogen gas.