open -a "Brave Browser.app" --profile-directory = "profile Name"
to get the profile name open brave and switch to the required profile then go to brave://version/ the look for Profile Path it will be the last word of it so it be default and profile 1 and 2 and so on
by the way when you want to look for command in brave search for it in chrome and it will work
i think the issue here --profile-directory=$PROFILE_PATH replace it with the profile name like Default or profile one and so on i guess this $PROFILE_PATH mean the path of your mac profile not the profile of the brave
sorry for late replay
hope that help and have a nice day