Eggs store very well when refrigerated and are naturally optimal in terms of physical volume. Buy eggs in bulk and store them in a large mixing bowl or other round container in your refrigerator.
Eggs have famously short shelf life, even in the refrigerator. They’re not going to last more than a month if you’re lucky. The egg cartons they’re sold in are already the most optimized way to store them. Moving them into something else doesn’t make any sense.