My system is very similar to yours, Jennie. I have buckets of grain and beans and big jars of dried fruit in the woodshed until we get a
root cellar built. I fill up quart jars to keep in the kitchen. Some things, like chickpeas, that we use a lot of have a bigger jar for the kitchen.
One of only two vegetables we store a lot of is potatoes. I'm hoping to have more success with carrots and beets next year, though. Potatoes get stored in my garbage can root cellar and I bring in a kilo or two at a time in a paper bag that gets stored in a cool corner of the kitchen in a bin under the counter.
We do have a few jars of dried leafy greens that get used in winter cooking that stay in the kitchen and always get used up every year. Mostly we eat fresh out of the garden and supplement with sprouts, microgreens, and store bought for the winter when the coldframes get sparse.
I need a better system for squash storage. I have a lot of spoilage right now because I don't have a cool place to store them.