If I were in this situation I would probably build a screen to sift the soil.
The one the fellow who owned our property left us was made of wire mesh, maybe this is called welded wire?
He used it to sift for arrowheads.
Anyway, I would sift slowly and pick out the plastic fragments as I sifted.
I feel the soil will be okay to use once the plastic has been removed.
If you are still concerned about the quality of the soil, why not grow mushrooms there and start adding organic matter that will build soil health?
Here are some threads that you or others might find interesting:
https://permies.com/t/120457/fungi-great-addition-homestead
https://permies.com/t/55431/fungi-soil-building
https://permies.com/t/154893/Mushrooms-veggie-garden