Like pp I've gone from, "why on earth is that a problem??" to "Ahhhh, I totally get it!"
I would talk to him, not about the work stash (which is totally normal!) but about the general division of labour.
Maybe it makes sense for you to shop most of the time if you're at home for longer in the evenings but he could contribute at least some of the time. Does he have input on deciding what you will eat each evening and organising it? I find that the biggest faff
As for He wouldn't do the weekly shopping - I would get constant phonecalls/video calls asking me about everything on the list e.g where it was in the shop, which brand I wanted, what to replace something with if they were out of stock. It's beyond stressful so I do it myself
He's an adult, with a (presumably) responsible job. He can work this out himself but if you never (or rarely) 'give' him the opportunity then he won't ever take responsibility for it.
Just tell him to use his best judgement and refuse to take the call. It's not rocket science to pick up a tin of Campbell's soup if they're out of Heinz. If he has to walk around the supermarket three times to find the right aisle then he'll know where everything is for next time. Or he can order online if he prefers.
Obviously if he takes full responsibility for laundry and you do all the shopping then that's a bit different but it seems like any household/family stuff is 'your job' and 'his job' is looking after himself and that's the actual root of the irritation