Usually, when we talk about the tarnishing of silver in air, we think of it as the reaction of silver with hydrogen sulfide in the air.
According to this account by Tim Burstein from Cambridge University, the main two reactions in dry air are:
$$\ce{4Ag(s) + O2(g) -> 2 Ag2O(s)}$$
and
$$\ce{Ag2O(s) + H2S(g) -> Ag2S(s) + H2O(g)}$$
The oxide layer is passivizing, so it remains thin and invisible. In contrast, the sulfide layer grows over time, giving rise to interesting changes in coloration.
[OP] However, when looking at the standard potentials, silver should not reduce hydrogen sulfide to hydrogen gas and silver sulfide.
The paper has a list of reaction steps with Gibbs energies of reaction. It makes the comment that standard potentials (electrochemical series) most often involve the metal ions in aqueous solution rather than metals salts. $\ce{Ag2S}$ is very insoluble, driving the process.
[OP] In this answer (https://chemistry.stackexchange.com/q/99812) it is said that the precipitation of silver sulfide drives the reaction to completion, however, silver is also a solid, and hydrogen also a gas, so there shouldn't be a reasion why silver should completely decompose in a hydrogen sulfide stream, rather reach a small equilibrium value.
If the reaction steps given above are a good representation of what happens, then there is no evolution of elemental hydrogen, and the argument in the answer to the related question is moot.
[OP title] Reaction of silver with hydrogen sulfide
I'm by no means an expert in this field, and am relying on the source I gave. If I understood the document, you should change your title to "Reaction of silver with dioxygen and hydrogen sulfide" or "Reaction of silver oxide with hydrogen sulfide" to reflect what might be happening in silver tarnishing.
[OP] However, since the Nernst equation breaks down (as there is no dissolved Ag+), I don't know how to calculate it. How to do this?
In the presence of humidity, tarnishing is much faster. In the presence of water on the surface, the process becomes an electrochemical one, allowing oxidation and reduction to happen at a distance.