Can be an expansion of already existing "fake town types", like you set a town in your nation as commercial and its ability is to gain access to auction house but at a higher % tax than capital perhaps

Or other downsiders/limitations when using auction house from those towns like limited amount of items you can buy daily from those towns / max amount of money you can spent from them daily

Nah 3 days cooldown is good

maybe certain amount of town claims to get ah

The problem with this is that everyone would set their capital to their fortress (to increase cost of it being sieged) and move their auction house. The "capital" would have to be based off of setting it in game rather than whoever owns the nation.(Ex: setting towns as developed, forts, advanced, etc)

That's honestly such a minor problem. Besides, who's stopping you from putting your fort as capital last second before getting sieged? That would allow you to still have /ah in the wanted town but also get the increased siege cost.

What about extra buyable /ah spot in each nation? The quantity of /ah spots would depend on how big the nation is or even the quantity of forts a nation has. Make that forts can't be /ah spots. Then, town requirements would be depending on the level of the town.

To avoid transporting stuff via /ah add a cd of 1-5 min with a preview on /ah of the "future items" to be sold

What I meant of preview is something like this:
https://cdn.discordapp.com/attachments/549722755428384780/1110646607046778930/image.png
The blue colored stuff could be checked like a normal item but not bought yet.

'To avoid transporting stuff via /ah add a cd of 1-5 min with a preview on /ah of the "future items" to be sold'

This is amazing