### Godot version

v4.1.1.stable.official [bd6af8e0e]

### System information

Godot v4.1.1.stable - Windows 10.0.19045 - Vulkan (Forward+) - dedicated NVIDIA GeForce GTX 1060 6GB (NVIDIA; 31.0.15.3179) - Intel(R) Core(TM) i5-8500 CPU @ 3.00GHz (6 Threads)

### Issue description

When connecting the `animation_started` signal from an animation tree, the connected method is always called twice.
This only occurs with the `animation_started` signal, the `animation_finished` signal is only emitted once.

This unfortunately makes relying on the signal impossible.

### Steps to reproduce

(See minimal production project)
- Use `animation_started.connect()`
- Print something out in the connected method (the example project prints the `anim_name` parameter)
- method is called twice -> two prints in the console

### Minimal reproduction project

[anim_tree_signal_bug.zip](https://github.com/godotengine/godot/files/12229864/anim_tree_signal_bug.zip)

The animation tree travels to the 'move' animation when `ui_accept` is pressed (see `anim_tree.gd`) and has print statements inside the methods connected to both the `animation_started` and `animation_finished` signal.

play_mode = p_play_mode;
}
AnimationNodeAnimation::PlayMode AnimationNodeAnimation::get_play_mode() const {
	return play_mode;
}
void AnimationNodeAnimation::set_backward(bool p_backward) {
	backward = p_backward;
}
bool AnimationNodeAnimation::is_backward() const {
	return backward;
}
void AnimationNodeAnimation::_bind_methods() {
	ClassDB::bind_method(D_METHOD("set_animation", "name"), &AnimationNodeAnimation::set_animation);
	ClassDB::bind_method(D_METHOD("get_animation"), &AnimationNodeAnimation::get_animation);
	ClassDB::bind_method(D_METHOD("set_play_mode", "mode"), &AnimationNodeAnimation::set_play_mode);
	ClassDB::bind_method(D_METHOD("get_play_mode"), &AnimationNodeAnimation::get_play_mode);
	ADD_PROPERTY(PropertyInfo(Variant::STRING_NAME, "animation"), "set_animation", "get_animation");
	ADD_PROPERTY(PropertyInfo(Variant::INT, "play_mode", PROPERTY_HINT_ENUM, "Forward,Backward"), "set_play_mode", "get_play_mode");
	BIND_ENUM_CONSTANT(PLAY_MODE_FORWARD);
	BIND_ENUM_CONSTANT(PLAY_MODE_BACKWARD);
}
AnimationNodeAnimation::AnimationNodeAnimation() {
}
void AnimationNodeSync::_bind_methods() {
	ClassDB::bind_method(D_METHOD("set_use_sync", "enable"), &AnimationNodeSync::set_use_sync);
	ClassDB::bind_method(D_METHOD("is_using_sync"), &AnimationNodeSync::is_using_sync);
	ADD_PROPERTY(PropertyInfo(Variant::BOOL, "sync"), "set_use_sync", "is_using_sync");
}
void AnimationNodeSync::set_use_sync(bool p_sync) {