So...

The tub of the dishwasher has been filling up with clean water between cycles. We usually run it every three days or so, and after three days there is an inch of water in the tub. Clean.

Searching I find that it is almost certainly the water inlet valve. Turns out it is a similar design to irrigation valves, with which I am very familiar. Solenoid pushes on diaphragm. If any crud is in there, diaphragm can't close properly. Leak. The DW is 20 years old, so doesn't surprise me this is failing.

I found the correct part number. The KitchenAid site wants $60 for it. Amazon original part is $40. Amazon also has cheap Chinese parts for $18. While the Chinese parts overall had decent ratings, several commented that theirs leaked. The $40 has a 1 year warranty, so I got that. I only want to have to fix this once, so it's worth it to me. Plus the frustration if it drips after I use the cheap part.

Watched a video about how to change out my exact part. Seems straightforward enough. We'll see after the part gets here. My experience is that they make it look easy, but it will take me 3x as long to do it as the video.

Sort of a high priority as the leak could get worse, and overflow the DW. Water on the floor is bad, especially since the dining room is on the other side of that counter, and it has wood floors.

If this goes well, I may order a new lower rack as ours is rusting in a few places (one tine that holds dishes has already come out). Upper rack is also, but still intact. I'd rather not get a new DW, but if enough is "wrong" with this one, that may be the ultimate solution. I was planning on keeping it until the pump gives out (which is probably as expensive as a new DW).