As xyz said, you assigned type variable with String.
Modified example to show what's going on:
extends Node2D
enum Type {NAV, PU, DROP, AP}
export(Type) var type
# Uncomment to throw error
#func _ready():
# type = "Throw error"
func on_hs_click():
print(type)
if type == Type.NAV:
print("No error")
func _input(event: InputEvent) -> void:
if event is InputEventKey:
on_hs_click()
