Have been using Brave for a long time now mine is up to date with no problems best to check your settings for things such as “Script Blocking” which can cause problems with drop down menus. I have not come across a problem with copy & paste. It may be worth going to “Reset settings” and restore settings to their original defaults .It could also be possible you have a corruption in the program which uninstalling and re installing may fix and can save a lot of diagnostic time but it does mean wasting time re installing apps & password etc
After uninstalling it’s always worth deleting the Brave folder that is left behind as that may contain problems before re installing
C://Users/[username]/AppData/Local