Hi Etan! Thank you very much for your appreciation, I'm really happy the project is taking shape from your perspective too !!
To answer your question, while it's hinted at the player that breathing underwater is required to go forth, there are no means to currently access such ability. However, you may go forth to roam this area once you've drained it, it's more of a teaser since you can't actually proceed to what's further (because that will lead to a whole lot of new areas haha), but you may find the whereabouts of Kristof. Interestingly enough, if that may tease your curiosity in how all of this connects, the location you find him in is right beneath the Stone Forest, coinciding with a specific event that he may be responsible for.
On the practical side, if you wish to find a way to drain this place, you'll find it in the Rat's Lair. Rodolphe had blocked a few cogs with a rock simply because the noise irritated him, you can remove it by interacting with it. It will have for effect to reactivate the draining system of the mines. This, of course, requires you to have access to this place as well. On the matter, I invite you to read the guide at the "Access the Rats Lair" part.
Good luck prisoner !