We are two people and run the dishwasher every 2-3 days, but it’s really nice to go lazy and throw a pot or pan in there, along with a few plates. You’re not gonna get away with that if you go with the little dishwasher.
Also, you’re basically using the same amount of energy and water either way. Probably less for the larger one if you compare them full.
They make instant recirculation pumps that cycle the water through the tankless in a loop and stop when the hot water gets back to the pump. We have one. If you don’t already have the return pipes for it, you’d need some additional plumbing work. (Either way, it should be professionally installed).
It’s the same system you’d have for a tank, but it can’t run all the time, or it burns up the heater. You have to trigger it. They make flow switches, but mine (new construction) was cheesed. I just set up a zigbee switch with a 1 minute timer to trigger the pump.
I’m not a contractor.
I’d poke around for rot and mark the edges to make sure it isn’t spreading. Maybe try to get up there and check after a storm.
It could absolutely be an old problem that stained the wood. I might make a 1-year calendar reminder if I didn’t see anything after a rain.