This doesn't say much, just that:
It’s not about SHA-256, it’s about the signature scheme, ECDSA. This will be broken way earlier and will make it possible to forge signatures and thus forge transactions
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.
There's also a paper that explains why quantum computing isn't a problem for bitcoin, let me put it right here:
https://arxiv.org/pdf/1710.10377.pdf.
Also, this thread:
I don't believe Quantum Computing will ever threaten Bitcoin.