Basically the idea is use hybrid. AES-GCM-256 or ChaCha20-Poly1305 for symmetric encryption (which is already PQ-safe), and ML-KEM looks set to become the standard for key encapsulation.

ML-KEM-768 is fast as an algorithm, faster than X25519 in terms of pure computation, but uses large keys, so has higher overheads on small payloads. Most of the time, they’re about equal, or the absolute time is so slow it doesn’t matter.

Most folks now are doing hybrid ML-KEM and X25519 to guard against undiscovered flaws in ML-KEM.

I believe ML-KEM is the standard algorithm for post-quantum asymmetric encryption. I think it's slower mainly because there's not good hardware support, but it shouldn't be a big deal because most encryption is hybrid where you only use the asymmetric crypto briefly to share a secret you can use for symmetric cryptography.

ML-KEM based on a lattice problem called "Learning With Errors", and there are similar lattice-based algorithms which have no known quantum speedup. Most traditional asymmetric encryption algorithms are based on number-theoretic assumptions like the discrete logarithm problem or the RSA assumption, which are broken by Shor's algorithm.

Symmetric cryptography (AES and SHA hash functions) are post-quantum resistant for now. Grover's algorithm technically cuts their asymptotic security in half, but that doesn't parallelize, so practically there is no known good quantum attack, and cryptographers and standards agencies tend to not worry about that. You can keep using those.

[edit: according to the sister comment posted simulataneously ML-KEM is faster than X25519. good to know!]

For something like PGP, any performance difference wouldn't matter. There is one message and the key agreement is done once. As long as things are fast enough to be imperceptible to the user we are fine.