Please consider to enable android feature called “adb cackup” for Brave browser.
ADB Backup allow to backup application with all data, and should allow to migrate whole Brave (with all settings and all data: for example all opened pages, bookmarks etc.). There is no root needed for this, but application should have this feature enabled.
It is default disabled for chrome and probably this is the reason why is also disabled for brave. But I found short instruction and it looks like it can be enabled very easy: