### 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.

String anims;
	for (int i = 0; i < get_input_count(); i++) {
		if (i > 0) {
			anims += ",";
		}
		anims += inputs[i].name;
	}
	r_list->push_back(PropertyInfo(Variant::STRING, current_state, PROPERTY_HINT_NONE, "", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_READ_ONLY)); 
	r_list->push_back(PropertyInfo(Variant::STRING, transition_request, PROPERTY_HINT_ENUM, anims)); 
	r_list->push_back(PropertyInfo(Variant::INT, current_index, PROPERTY_HINT_NONE, "", PROPERTY_USAGE_STORAGE | PROPERTY_USAGE_READ_ONLY)); 
	r_list->push_back(PropertyInfo(Variant::INT, prev_index, PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NONE));
	r_list->push_back(PropertyInfo(Variant::FLOAT, time, PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NONE));
	r_list->push_back(PropertyInfo(Variant::FLOAT, prev_xfading, PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NONE));
}
Variant AnimationNodeTransition::get_parameter_default_value(const StringName &p_parameter) const {