Whilst I agree that you shouldn't have left your dishes in the dishwasher, the owners should have left one or two tabs to keep you going while you got your own while there.
We've been taking UK cottage holidays for nigh on 30 years. It's been hit and miss.
Having spoken to owners, over the years, it's become apparent that quite a few folk feel that ( like at breakfast time in a hotel) that ' I've paid for it, we'll take it.'
So many cottage owners don't like to leave a box of dishwasher tabs, laundry tabs, fabric conditioner, salt, pepper, washing up liquid, even tea towels as some folk just take it all! Just because they feel entitled to.
We always take our own provisions , however, we once flew to Inverness ( we're in Kent) as it was too far to drive ( I'm scared if motorways so driving is down to my husband) and we hired a car to our remote cottage, with young children.
There was barely anything. One medium sized saucepan, one small baking sheet, half( yes!) a scouring pad, half ( yes again!) dishcloth and one grill pan.
No dishwasher tabs, washing tabs, fabric conditioner, washing up liquid, soap, shower gel, toilet cleaner , clothes line, drier, pegs and one toilet roll.
Given that we'd flown, we didn't stock up... just assumed.
It was about 12 miles to a convenience store.
Basically, take a few essential bits if you can and grab more bits before you get there.