How do I remove a Faction (specifically, the Stronghold) from the available options entirely?

As a temporary solution to ban a faction, I can suggest manually adjusting each random town through the map editor. Each random town has a BannedRaces parameter in the Properties window, where you can ban factions.

But if I understand you correctly, this means that you need to "mod" each map on which you plan to play in this way, and after the need for the ban disappears, you need to return "everything to its original state" (or just save the necessary changes separately and then revert them).
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Still, thank you for the answer, it will also be useful 👍