I know you asked about panniers, but I haven't used them. Here are other suggestions:

I bunged a medium sized plastic basket on my Boardwalk. I can quickly take it off and bring it in the store with me. I only did it three times to the grocery store, but it didn't fall off.





But usually when make small grocery run or have items to take to work I take my utility bike with Wald folding baskets. I wonder if they would work on a 20-inch folder.



For bigger loads, I take my trailer which I can also lock up outside the store.



But for compactness, I'd look at a small, kid or pet trailer that folds and collapses. It can be brought in and put a cart...or if it has an attachable front wheel, like for jogging, it can be used as a shopping cart itself.