Mineral water may have a small amount of trace minerals, but it has basically zero electrolytes at relevant physiologic concentrations. Functionally, there'd be almost no difference between distilled and mineral water fasting with respect to electrolyte management.

Imbalances in sodium, potassium, magnesium and calcium can get VERY serious very quickly. Mineral water does not really have relevant concentrations of those.

I think you're conflating the idea that distilled water isn't particularly good for you since it starts leaching out the trace minerals from parts of your body, with the entire concept of electrolyte management. These are VERY different things, occurring with VERY different relevant concentrations... like at least 1-2 orders of magnitude.