This is why CC0 should not be used for code. Its public license fallback explicitly does not give patent rights. Compare that to MIT which implicitly does by saying you can use the software however you want. CC0 literally has this clause in the public license fallback.
No trademark or patent rights held by Affirmer are waived, abandoned, surrendered, licensed or otherwise affected by this document.
This is why CC0 should not be used for code. Its public license fallback explicitly does not give patent rights. Compare that to MIT which implicitly does by saying you can use the software however you want. CC0 literally has this clause in the public license fallback.