### 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.

sync = p_sync;
}
bool AnimationNodeSync::is_using_sync() const {
	return sync;
}
AnimationNodeSync::AnimationNodeSync() {
}
void AnimationNodeOneShot::get_parameter_list(List<PropertyInfo> *r_list) const {
	r_list->push_back(PropertyInfo(Variant::BOOL, active, PROPERTY_HINT_NONE, "", PROPERTY_USAGE_EDITOR | PROPERTY_USAGE_STORAGE | PROPERTY_USAGE_READ_ONLY));
	r_list->push_back(PropertyInfo(Variant::BOOL, internal_active, PROPERTY_HINT_NONE, "", PROPERTY_USAGE_STORAGE | PROPERTY_USAGE_READ_ONLY));
	r_list->push_back(PropertyInfo(Variant::INT, request, PROPERTY_HINT_ENUM, ",Fire,Abort,Fade Out"));
	r_list->push_back(PropertyInfo(Variant::FLOAT, time, PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NONE));
	r_list->push_back(PropertyInfo(Variant::FLOAT, remaining, PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NONE));
	r_list->push_back(PropertyInfo(Variant::FLOAT, fade_out_remaining, PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NONE));
	r_list->push_back(PropertyInfo(Variant::FLOAT, time_to_restart, PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NONE));
}
Variant AnimationNodeOneShot::get_parameter_default_value(const StringName &p_parameter) const {
	if (p_parameter == request) {
		return ONE_SHOT_REQUEST_NONE;
	} else if (p_parameter == active || p_parameter == internal_active) {
		return false;
	} else if (p_parameter == time_to_restart) {
		return -1;
	} else {
		return 0.0;
	}
}
bool AnimationNodeOneShot::is_parameter_read_only(const StringName &p_parameter) const {