Ok, here's the skinny on the dishwasher:
I don't want to jinx it, but I think after having taken apart the kitchen sink trap (which is now leaking, naturally, but that's another job for another day), to find nothing nefarious; and disconnecting the dishwasher drain hose and inspecting it, draining it, and not checking for kinks (because it goes around the back of an integrated dishwasher, how am I supposed to do that??); then reconnecting everything...
I read online that sometimes there's a temporary fault in the electronics board that can make the dishwasher think there's a blockage when there isn't (hence it won't drain). So, I did a factory reset, then ran a short wash with no dishes and no detergent, listening out for whirring or grinding noises from the drain pump just in case. After 45 minutes, cycle done, opened up the dishwasher and... VOILA no standing water!
If you haven't fallen asleep by now and have read this far, I basically turned it off and turned it on again.
I am cautiously optimistic but time will tell.
I am now available for dishwasher repair services, for which I will charge an exorbitant fee.
ps. but don't ask me to fix your kitchen sink trap, because I'll make it worse.