Let's talk about our Red Rush strategy...

To ensure that the opponents are on a more or less equal footing, either allow Blue to buy out the growth (which will appear in the Castle, not in the mine), or have both fight without growth, or Red must ensure a chain of supply for its growth (i.e., first capture a Castle, and then transfer new troops there).

Firstly, the goal of "allowing Blue to buy out the growth" is questionable. Whether or not Blue will have this opportunity should depend on how the opponents have played up to that point.

The correct goal is "To ensure that the opponents are on a more or less equal footing." But this goal is fully resolved by the stipulation that the presence of growth in the army should not affect the outcome of the battle.

I am simply pointing out that the existing stipulation (the presence of growth should not affect the outcome of the battle) already puts the opponents on the most equal footing when it comes to capturing cities.
If Blue is capable of offering at least some resistance, then Red is already obliged to take the city with what it has at the beginning of the week, and then ensure a chain of supply. This is already in the rules.

But with the current wording, where cities are treated differently, it turns out that Blue may not defend the cities at all, and Red must still deal with the chains.
And if he doesn't sort out the chains, he cannot, for example, use his last hero in the chain to take an empty intermediate city and settle there with growth. And Blue will retaliate with growth.

For now, it still looks not entirely clear.