A hash is not a password store
SHA-256 is designed to be fast, which is exactly the wrong property for storing passwords. A modern graphics card computes billions of SHA-256 hashes a second, so a leaked table of hashed passwords is a table of passwords with a delay attached.
Password storage needs a function designed to be slow and memory-hard — bcrypt, scrypt or Argon2 — with a per-user salt. Those exist specifically to make the guessing attack expensive. Using a general-purpose hash instead is the most common serious mistake in this area, and it is not fixed by hashing twice.
What SHA-256 is genuinely good for is checking that data has not changed: verifying a download, detecting a modified file, building a content address. In those uses, speed is a benefit.