Actually, all packaging materials can be recycled in the following way:
- Burn it to energy, releasing carbon dioxide and preferably using that energy to create electricity or district heating (or ideally both in combined heat and power generation)
- Let a tree grow in a forest, capturing the released carbon dioxide
- Chop down the tree
- Manufacture more of the packaging material from the tree
Yes, even plastics can be made this way. For cost reasons, most are made from oil today but there's genuine progress in making all sorts of fuels and plastics from trees.
Besides, packaging materials are not a genuine problem. Usually the weight of the packaging is about 1/20 the weight of the food inside the packaging. If the packaging is plastic, making one gram of plastic creates about 2.6 grams of CO2 emissions. So packaging of 200 grams of food (10 grams of packaging) creates 26 grams of CO2 emissions.
For example, one kilogram of pasta creates 1.3 kilograms of fossil CO2 emissions. So 200 grams would create 260 grams of CO2 emissions. Compare that to the 26 grams of CO2 produced by creating the packaging material.
The answer to minimizing your CO2 emissions from food is to prefer low-CO2 food items and avoid meat. For example, a very small amount of meat in a "recyclable" (I hate that word because by burning it and growing trees every organic material can be recycled) packaging is far worse to the environment than an equivalent amount of vegetables in a non-"recyclable" packaging.
You have already minimized your emissions by choosing to be a vegan. There's nothing more to do.