Autofill Passwords on iOS does not work at all

Brave added password sync between PC and iOS devices, but it does not work. Synchronization is working, I see my passwords on my iPhone. On the other hand, I cannot autofill them. I’ve tried to disable iCloud Password Manager, in that case I cannot autofill any password and each field I need to fill manually. I guess there has to be an option to change from iCloud Password Manager to Brave password manager, like Microsoft Edge or Google Chrome changes default password manager on iOS.