[1] - https://tools.ietf.org/html/rfc2898#section-5.2 [2] - https://en.wikipedia.org/wiki/Bcrypt
It really depends on what the person means. Yes, single sha-2 hash is pretty useless. But that's often not what's really happening. For example libcrypt is used in many cases with the default $6$ format which uses thousands of rounds of sha512. That's still "password hashed with sha-2".
You could upgrade it for new users, but for old ones? (e.g. I don't change passwords often)
Of course, that only works for active users - it won't upgrade anyone that never logs in. Depending on just how weak the old hash is, you may want to eventually cut off any lingering un-upgraded accounts: just forget their old hash, requiring them to go through your password reset process should they ever come back. If you've left it long enough, those accounts will probably never be used again anyway, so that should be NBD.
As the sibling comment points out, SHA-2 is worthless for storing passwords. A GPU can crank through an obscene number of SHA-2 hashes per second. Bcrypt is is intentionally much slower and harder to use a GPU to brute force. The two algorithms are almost totally unrelated and it's concerning they were mentioned together.