Where did you conclude that once SHA256 is broken, we'll upgrade to SHA384? If SHA256 becomes broken, which is a doomsday scenario, we shouldn't use neither SHA384 nor SHA512 as they all belong to SHA-2.
This is a very common misconception that people do when talking about the security threat of quantum computers to btc & co. The main issue is not about the encryption algorithm, but instead of signature algorithm as it was mentionned in the link.
If a paper says the threat is non existent or is centuries away, feel free to believe them. But ask the authors how much money they will bet on their timeline and I am happy to bet against them