I backed up my phone, and it didn’t restore any of the passwords I had.

Passwords aren't listed as what iCloud backs up -- What does iCloud back up? - Apple Support. However, your passwords are stored in your iCloud Keychain providing that's what you were using to store them. Do you know if that was enabled?

Try Settings/Your Name/iCloud and slide off syncing. Wait a few minutes and then slide syncing on. Allow time for syncing to occur.

Last resort - have you tried signing out of iCloud and then sign back in?

See if anything here helps.

Frequently asked questions about iCloud Keychain - Apple Support.   

Everything you need to know about iCloud Keychain - iMore.