Literally found the same issue in a password system, on top of passwords being clear text in the database... cleared all passwords, expanded the db field to hold a longer hash (pw field was like 12 chars), setup "recover password" feature and emailed all users before End of Day.

My own suggestion to anyone reading this... version your password hashing mechanics so you can upgrade hashing methods as needed in the future. I usually use "v{version}.{salt}.{hash}" where salt and the resulting hash are a base64 string of the salt and result. I could use multiple db fields for the same, but would rather not... I could also use JSON or some other wrapper, but feel the dot-separated base64 is good enough.

I have had instances where hashing was indeed upgraded later, and a password was (re)hashed at login with the new encoding if the version changed... after a given time-frame, will notify users and wipe old passwords to require recovery process.

FWIW, I really wish there were better guides for moderately good implementations of login/auth systems out there. Too many applications for things like SSO, etc just become a morass of complexity that isn't always necesssary. I did write a nice system for a former employer that is somewhat widely deployed... I tried to get permission to open-source it, but couldn't get buy in over "security concerns" (the irony). Maybe someday I'll make another one.