What usually happens to the symmetric (session) key after decrypting an email? Can the key be recovered if changing private keys?

The general and normal solution, as commented, is that the recipient retains old privatekeys to decrypt old messages, even though the corresponding publickeys have expired (or even been revoked). In fact in some organizational settings the privatekeys used for decryption are backed-up by the organization so that email can still be read if the individual(s) to whom it was sent leave(s) or die(s). (In tech this is sometimes called a 'bus factor' -- if an employee with key information and/or abilities is hit by a bus and killed, can the organization continue operating without them?) In contrast privatekeys used for signing are not subject to this requirement; if a person leaves, the new person should publish a new signing key which recipient(s) accept as valid, but should not be able to make it appear the old person signed something they actually didn't. BTW these approaches apply to both PGP and S/MIME, although the method of publishing a new key differs somewhat.

GnuPG (one implementation of PGP) has a feature intended for a slightly different case: see --show-session-key et seq in https://www.gnupg.org/documentation/manuals/gnupg/GPG-Esoteric-Options.html . The idea is that if you are forced to disclose some of your email -- for example in a lawsuit -- instead of giving the privatekey that allows decryption of all your (past) messages you can give the DEK(s) for a specific message(s).