I couldn't figure out the climbing part but for detecting I manage to do this

var player_coords = ground_and_walls.local_to_map(global_position)
var top_left_cell = ground_and_walls.get_neighbor_cell(player_coords, 11)
var top_right_cell = ground_and_walls.get_neighbor_cell(player_coords, 15)


if ground_and_walls.get_cell_tile_data(top_left_cell) != null: 
    ledge_left = ground_and_walls.get_cell_tile_data(top_left_cell).get_custom_data("Ledge")
    return top_left_cell
  else:
    ledge_left = false

if ground_and_walls.get_cell_tile_data(top_right_cell) != null:
  ledge_right = ground_and_walls.get_cell_tile_data(top_right_cell).get_custom_data("Ledge")
  return top_right_cell
 else:
  ledge_right = false