signatures are more urgent but hash functions are not threat proof either.

All hash functions based on universal-hashing have been shown to be threatened by Bonnetain 2021. It's not impossible the same will happen with Merkle Damgard constructions like SHA will have simmilar algorithms.

But worry not, there are many post-quantum secure hash functions in academia being discussed. They will be ready soon - many many years before quantum computers will have bit lengths long enough