Shor's algorithm also solves the discrete logarithm problem, so it also theoretically breaks Elliptic Curve Diffie-Hellman. That is, it breaks both of the main

Shor's algorithm also solves the discrete logarithm problem, so it also theoretically breaks Elliptic Curve Diffie-Hellman. That is, it breaks both of the main types of key-exchange algorithms (as well as SRP) in use today with TLS. (Not PSK, although that in turn isn't usable in a limited-trust environment like the broader internet.) My understanding is that any use of post-quantum crypto today is layered on top of existing crypto (so breaking one is insufficient to compromise the channel), in large part due to the relative immaturity of the field that you've mentioned. The threat model here is not necessarily that we expect anyone to have sufficiently capable quantum computers (and/or algorithmic breakthroughs) in the immediate future, but that a potential adversary might store some encrypted comms that they can later decrypt. Perfect forward secrecy doesn't protect you against an algorithmic break.