I'd only get basics on the Saturday (tea bags/coffee/milk/bread). You might arrive and find that salt, pepper, oil etc has been left but equally there might be nothing. Best to do a big shop when you know what you need.
Oh yes, travel snacks essential I'd also take a loo roll or at least some tissues, we've turned up at places with none provided and after a long drive you might want some! Presumably you'll be taking shower gel etc so at least you'll have something to wash your hands with if there is no soap.
Things that aren’t worth buying for a weekend, like: Salt and pepper Tea bags Coffee Sugar (if you take it)
Check if they supply tea towel, oven gloves, washing up liquid, washing up sponge / brush, bin bags etc as it’s easy enough to shove in yours if they don’t.
I usually take something easy for supper (eg frozen stew that can defrost on the journey) and enough milk and cereal for breakfast. Then either shop there, or (usually) arrange for an online delivery to arrive on the first morning.
Good call on the loo roll, condiments, oven gloves, bottle openers etc. I think I'll pack a bag of that stuff separately, so I can leave in the boot if not needed. I can see clocks in the pictures and I have my phone so should be ok there.
I'll be arriving for breakfast or brunch I think. So I'll probably have a cuppa (on the la di da "roof terrace with scenic views" dontachaknow!) when I get there, then take myself out for something to eat and get my bearings, get some food in etc.
Take some tupperware style containers for any left overs you want to put in the fridge or take away if you are planing picnics. I found these ones are th one thing always missing. Oh, and a decnt pocketknife. Well, apart from one SC where they had the whole picnic hamper/blanket/boxes etc down to a T.
I agree with knives but I normally just bite the bullet.
Google the opening times of any supermarket in driving distance or ask the landlord where you can shop.