Run without any internet access (including during setup).
Can be controlled over LAN via HomeAssistant.
Mop.
5GHz wifi support and multiple floor capability would be a big bonus, but not a deal-breaker.
Basically, I'd like to get one, and see how I get on with it.
I'm happy to get something old/budget, to help me work out what I want in a "forever" vacuum.
Happy to buy second hand, and happy to flash/jtag/hack, so long as the procedures are reliable.
Definitely go with valetudo, they have a good robot buying guide for 0-cloud vacuums. No flashing needed, but you may need to do some SSH. Only downside I think is that valetudo doesn't support multiple floors.