Brave Settings, Sync in the settings tree. In the sync settings pane, go to the Additional Settings dropdown control at the bottom of that pane and expand it. Search for Autofill. The first Autofill entry is for passwords, expand it. Throw the toggle for Offer to save passwords to on. If you also wish to have auto sign-in for sites for which you're saving passwords, then throw the toggle for Auto Sign-in to on.
Even when both are on you can decline to save password information for specific sites, and Brave will remember those that you do not wish to save passwords for as well as the passwords for those you do. There is also a search box at the top if you need to search for a specific site in those lists or password in those lists to deal with either later.
Brian - Windows 10 Pro, 64-Bit, Version 1903, Build 18362
Many of the insights of the saint stem from his experience as a sinner.
~ Eric Hoffer