We want to migrate our userbase from bcrypt to argon2.
I was planning on an approach that migrates all hashes immediately to argon2; "old" users would have an argon2'd hash of their bcrypt hash of their password. New users (and users that logged in) would get updated so their argon2 hash of their password was what was saved.
My problem is: to compare hashes in the legacy case, I have to be able to generate a bcrypt hash first then an argon2 hash. But the bcrypt hash comparison requires information from the password hash itself (salt etc.) to generate a matching value (which can then be hashed with argon2).
If I want to use this approach, do I have any option other than extracting and storing the bcrypt salt somewhere outside the password field?