Built this and it works. Edge cases and "what if" questions in the comments are welcome — I'm still learning from them.

import { createStore } from "stroid"
import "stroid/persist"
import "stroid/sync"

createStore("cart", {
items: [],
total: 0
}, {
persist: {
key: "cart",
allowPlaintext: true,
version: 1,
onStorageCleared: ({ reason }) => {
console.warn("Cart cleared externally:", reason)
}
},
sync: {
channel: "cart-sync",
policy: "insecure",
conflictResolver: ({ local, incoming, localUpdated, incomingUpdated }) => {
return localUpdated > incomingUpdated ? local : incoming
}
}
})