PFS is not magic, it depends on exactly the same type of trapdoor algorithm as other asymmetric cryptography but using randomly chosen keys which are then forgotten. Forgetting the keys + Breaking them being too hard = Forward Secrecy. If someone finds out the key later, they can decrypt the messages, just as if they'd been told it at the time.

A Quantum Computer that breaks say, 2048-bit RSA also breaks the PFS-enabled Diffie-Hellman style key exchanges, it's almost exactly the same trick, a variant of the Discrete Logarithm Problem.

That's only really useful in key exchange scenarios (DH/ECDH). A lot of implementations use RSA or similar to directly encrypt packets of information, though it's generally not recommended for reasons such as this.

That doesn't help if the past key is cracked.