In what sense do you consider SHA-256 superior to SHA-1?
If you're looking for preimage resistance, unless your passwords contain more than 128 bits of entropy, I suspect bruit forcing your password is still faster than a preimage attack on SHA-1, and will probably remain so for at least a decade. Collision attacks aren't useful for passwords (attacker chooses two passwords such that they have the same hash... I can't imagine a threat model under which this is useful to the attacker if that hash doesn't match any target's password hash. Maybe there is such a threat model, but it has to be a very outside-the-box attack.)
If you're worried about effort needed to bruit-force the password, use Argon2 or another memory-hard password hash/KDF.
If you're looking for preimage resistance, unless your passwords contain more than 128 bits of entropy, I suspect bruit forcing your password is still faster than a preimage attack on SHA-1, and will probably remain so for at least a decade. Collision attacks aren't useful for passwords (attacker chooses two passwords such that they have the same hash... I can't imagine a threat model under which this is useful to the attacker if that hash doesn't match any target's password hash. Maybe there is such a threat model, but it has to be a very outside-the-box attack.)
If you're worried about effort needed to bruit-force the password, use Argon2 or another memory-hard password hash/KDF.