Seems there's work going towards, or at least the idea is being explored, adding PQC to OpenPGP.
https://www.ietf.org/id/draft-wussler-openpgp-pqc-00.html
https://datatracker.ietf.org/meeting/113/materials/slides-11...
>If you insist on using Pass, I highly recommend using a separate PGP key just for Pass.
Will guess that's how most people use it already. Separating keys for usage is afterall something core in PGP.