>SHA-1 has been known to be vulnerable since 2005, and even in 2012 SHA-2 and SHA-3 were recommended.
FYI, the requirements for a password hash function is significantly different than for a cryptographic hash function. the vulnerabilities you're talking about doesn't affect any of those properties. password hashes only need to have preimage resistance, and (more importantly) be slow as to limit offline attacks.
This is pretty much correct. It doesn't much matter what cryptographic hash you use to store secrets, and all of the general-purpose cryptographic hashes are bad password hashes. Salted SHA-3 would not be materially better than salted SHA-2 here.
FYI, the requirements for a password hash function is significantly different than for a cryptographic hash function. the vulnerabilities you're talking about doesn't affect any of those properties. password hashes only need to have preimage resistance, and (more importantly) be slow as to limit offline attacks.