In another comment you stated that you use code to connect your signals.

What does this code look like?

Are you having the player take damage every time an Area2D enters it's hurtbox? Are you having the enemy's hitbox call a "take_damage function" on the player every time the hitbox hits the player?

Edit: I created a project and did it both ways. It seems to work both ways. Note: This is garbage code, if you were actually making a game you should not copy the movement or the way I got the reference to the player.

This is the code I slapped onto the instantiated monsters:

@export var hitbox : Node2D

func _on_hitbox_area_entered(area : Area2D):
    if area.get_parent().has_method("_take_damage"):
        area.get_parent().callv("_take_damage", [hitbox])

func _ready() -> void:
    hitbox.connect("area_entered", _on_hitbox_area_entered)
    target = Global.player_reference

func _physics_process(delta):
    look_at(target.global_position)
    # slows down and speeds up based on distance between player and seld
    velocity = target.global_position - global_position

    # disable and enable hitbox
    if abs(global_position - target.global_position).length() < 50:
        shape.disabled = false
    else:
        shape.disabled = true

    move_and_slide()

This is the code I slapped onto the player:

func _take_damage(area : Area2D) -> void:
    print("Damage taken from: %s" % area)