Map Marker Overhaul lets you remove the quest arrow from the local map while keeping it on the world map, or from both maps. It has no setting for removing it from the compass, but I recommend Darnified UI for that.
Personally I find it most immersive to disable the quest arrow from the compass and local map, but keep it in the world map, as that is similar to putting a mark on a paper map in real life. Especially with Map Marker Overhaul's other immersive map options of removing the player's you-are-here icon from the world map, and not centering the world map on the player when opening it (but instead remembering the last position). I urge people to try those options, as they feel more immersive than I would think.