AnotherGame is a mod for ToE 3.1.

So, if we follow a purely market-based approach, the price would be around 35,000. I get a fifth of that. But the payback period shouldn't be longer than a week, and the upgrade costs should be the same for everyone. In terms of gold, that's 7,001 gold. But the number isn't very appealing, so I increased it to 7,500. However, in the end, the market only adjusted the cost of mines by 2,500, not 30,000 :) +
Maybe we can analyze it with a specific example?
Necromancer? Elf? Would it be profitable for an Elf to upgrade a lumber mill?

No, no. The market-based approach cannot be applied in the same way to income. No one will ever upgrade mines for 35,000. Because the shortage of 1-3 resources is usually discovered on the same day they are needed. This is the point of the market: you can exchange any amount of resources at once, and you can get rid of any surplus, not just gold.
In your case (mines), this is not the case. Therefore, it is more logical to apply the warehouse approach.
As for gold, its payback period should be 5 days (like the Capitol branch), since there is no exchange here.

Let's analyze it for the Elf. 5,000 is the maximum price I am personally willing to pay for a wood shortage. The same applies to mercury for the Necromancer. The warehouse is slightly more expensive (+5 stone), but its advantage is that it can be used at any time, including at the beginning of the game, and not only when the mercury mine has already been captured (and development only speeds up the growth). Plus, a mine can be easily captured, while a city is more difficult to miss.