Bikepacking is traveling light. But regardless...
Carry one large thin bag that can hold all the others. Put them all in the large one, go to the store, ask to stash your bag while shopping (so they know you aren't hiding items you haven't paid for yet in it). Retrieve it when you pay and leave.
A wheeled trolley to hold this large bag is probably excessive, but I have seen shopping panniers with wheels - two of those might fit your needs.
Considering the pictures others posted along with their replies, I would think full front and rear panniers is impractical for this, but the bikepacking picture looks quite reasonable.
