Here is the script for Safari:
Note: "You must enable the 'Allow JavaScript from Apple Events' option in Safari's Develop menu to use 'do JavaScript'."
tell application "Safari"
repeat with t in tabs of windows
tell t
if URL starts with "http://www.youtube.com/watch" or URL starts with "https://www.youtube.com/watch" then
do JavaScript "
var player = document.querySelector('video');
player.currentTime = player.currentTime + 10;
"
exit repeat
end if
end tell
end repeat
end tell
I can't help you with the Brave browser as I don't have it installed, but you can try to add it to the Script Editors Dictionary (under windows) to see if it is scriptable and if so, what the commands are. See: change browser in script to work with brave browser instead of safari - #2 by Caliguvara