(But note: absent something like that, it in fact is possible for Signal to prove that you’re communicating with the same identity you initiated with. That’s the whole point of authenticated key agreement, which is not something that PGP can natively perform.)
Is that not tofu, which is easy in many crypto systems?
In other words: you always need to perform OOB identity verification, regardless of your messaging system of choice. There is no way around this; it’s a fundamentally social and UX problem rather than a cryptographic one. But this doesn’t change the fact that, once you have a trusted identity, Signal’s MITM protections are significantly stronger than PGP’s (including forward secrecy, as noted before).
Web-of-trust alleviates that, to some extent.
(I think WoTs can solve these problems. But PGP's implementation has been so far the most ambitious tried by a semi-large audience, and it didn't hold up. We need a better starting point.)
This attack will be noticeable: there will be a message warning the user that the cryptographic keys have changed on the other end. You know what else generates these warnings? Reinstalling WhatsApp, switching phones... They're basically noise to users by now due to alarm fatigue. How many users even know what that this key stuff means anyway? How many people even use the built-in key verification function which consists of just scanning a QR code? I've yet to meet a single person who cares about any of this stuff.
(Signal and WhatsApp also have forward secrecy properties that PGP, as an ecosystem, is nowhere close to providing. PGP very much still operates under the "one master key that you must never ever lose or disclose" paradigm.)