Yes, the veggie bags are better.
However, the boxes wrapped in paper might need to be wrapped as well. Those don’t seem particularly airtight.
Poor man’s vacuum seal:
Put the item in a triple ziploc. Insert straw to one side of the opening.
Close the ziploc all the way to the straw compressing the bag to remove as much air as possible.
Then suck the rest of the air out of the bag thru the straw; pull out straw quickly and close the rest of the ziploc.
Can’t remember where I read about that trick, but it was many years ago. Maybe these days you’ll want to use a syringe with a plastic tube on the end.