I wish there would be something like this in the UK but with county instead of state. E.g. swindon.wiltshire.uk or sheffield.southyorkshire.uk

I was hoping there would be something funny like twatt.worcs.uk or reading.berks.uk ... That aside, what would you do with such a domain? You could register x.uk with Nominet UK presumably. Just a small matter of the bill.

Buy the domain names then and offer those services.

The US state ones are just sub-domains. city.state.us isn’t a TLD.