Live trays of shoots and sprouts are sold all over the US, but obviously the stores you go to may vary. They look like this with a clamshell and cellophane top.
Most ship with plastic packaging, as you noted, but they still have aerated ceiling because it's obviously necessary.
If you want permeable packaging that won't suffocate delicate shoots, you want packaging with a sturdy bottom to prevent water drainage, but a porous top with air flow. Sugar resin bottom, and plant fiber top. That will get you what you need, and last weeks.
Plenty of manufacturers out there who will sell you any molding you need of these things at scale.