There isn't a lot of lignin in leaves.
Lignin is the tough stuff that holds the plant up.
The non-degradable plants would be the wheat and rice crops mostly (or exclusively -- we decide as a matter of policy).
What is left after harvest can be plowed back into the soil. The non-lignin parts would degrade, leaving the lignin skeleton to hold moisture and nutrients, improving the soil. Currently, one of the best soil improvers is biochar, used to make
terra preta. A non-degradable lignin would have similar properties.
Quite a bit of the soil is already made of non-biodegradable materials like quartz, feldspar, mica, and other minerals. If your bits of plastic bag were shredded finely enough (into sand grains) they would indeed be a decent way to sequester carbon in the soil. Unfortunately, they weren't made from carbon in the air, so it is not a solution to the climate crisis. But lignin is made from carbon in the air.
If we had policies that made it cost effective for farmers to char the crop remains and return it to the soil, then bioengineering would not be part of any solutions. But I thought it would be an interesting topic for this group to think about. Are there genes out there in the wild that already produce carbon containing molecules that do not biodegrade? The beauty of lignin is that it is already needed by the plant, so no extra metabolic cost is wasted by the plant, and crop productivity should not suffer.