How can you divide the feather board into different worlds? For example: when I was in Spawn it would show up the Spawn board and when I moved to PvP area it would automatically switch to PvP board
That should theoretically be possible, however I have not personally tested this myself. I do intend to test this, however - for a server that I manage.
That's entirely possible, refer to this thread here for more information. https://www.spigotmc.org/threads/feather-board-different-scoreboard-per-world.265653/