Someone gets access to your PGP private key(s). What to they get?

1. Access to any of your future incoming PGP protected email that they can see in transit.
2. Access to your archived email.
3. Access to any of your past incoming PGP protected email that they recorded in transit.

Forward secrecy addresses the third issue. Some process is used to come up with a temporary key known only to you and your correspondent (e.g. Diffie–Hellman key exchange). That key is used to encrypt the message. After the message is transferred and decrypted that temporary key is destroyed. That way any of your protected emails intercepted by someone will stay protected unless that someone figures out how to break the underlying crytographic algorithm(s). That is normally much harder than stealing your private key(s).

Real time forward secrecy requires a end to end, bidirectional communications channel to establish a temporary key. Email is inherently unidirectional and allows the email to be stored and forwarded. Old emails tend to be relatively valuable and are often archived. That makes forward secrecy pointless in practice. Whatever method is used to get the private keys could be used to get access to the archives.

You can get the result of forward secrecy by using PGP with a bit of forethought. You and your correspondent(s) would create subkeys specifically for the discussion that is to be forgotten. Those keys would be used for that discussion for as long as could be considered prudent. That might be many years; sometimes the only requirement is that a discussion can be forgotten. Then you and your correspondent(s) delete the subkeys. That will also permanently remove access to any archived emails. wherever they ended up. A system that provided real time forward secrecy would need a separate archive system and thus would likely require some careful deletion if such an archive was kept. The PGP case allows a complete archive with no extra risk. This is a benefit of the PGP encrypt once scheme.