Good old SSH managed to update ciphers. This is certainly easier if Server and client can negotiate, but it’s not impossible for GPG. You could start by adding better modes as an option, later make them default and ask for confirmation when decrypting an old message format. If I read the vulnerability description correctly, it allows stripping the message authentication signature and then trick the client into decoding it. So any message sent with a modern cipher or just requiring message authentication by default would have substantially mitigated the attack.

It is possible, but note that SSH is interactive and always had multiple ciphers. On PGP, as far as I can tell, there is no field for the cipher used. So you somehow need to introduce that field somewhere, but be able to deal with files that do not have that field. Possible but very tedious. The non-interactivity seems like it makes it harder to 'negotiate' a version. As there is no way to get clarification.

At the same time, you need to be careful against downgrade attacks.

Sure, as I mentioned, it’s easier if you can negotiate ciphers. But on the upside, there’s no downgrade attack. If the sender uses a modern cipher, the receiver either supports it or can’t decode the message. Still, that’s not a hard reason to not introduce protocol changes like new ciphers and a new field. Funny that you mention that since currently GPG on my Ubuntu spits out warnings about some feature it does not understand in files encrypted with a newer GPG on my fedora. This actually trips up some of my tooling.