### 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.

}
AnimationNodeTimeScale::AnimationNodeTimeScale() {
	add_input("in");
}
void AnimationNodeTimeSeek::get_parameter_list(List<PropertyInfo> *r_list) const {
	r_list->push_back(PropertyInfo(Variant::FLOAT, seek_pos_request, PROPERTY_HINT_RANGE, "-1,3600,0.01,or_greater")); 
}
Variant AnimationNodeTimeSeek::get_parameter_default_value(const StringName &p_parameter) const {
	return -1.0; 
}
String AnimationNodeTimeSeek::get_caption() const {
	return "TimeSeek";
}
double AnimationNodeTimeSeek::_process(double p_time, bool p_seek, bool p_is_external_seeking, bool p_test_only) {
	double cur_seek_pos = get_parameter(seek_pos_request);
	if (p_seek) {
		return blend_input(0, p_time, true, p_is_external_seeking, 1.0, FILTER_IGNORE, true, p_test_only);
	} else if (cur_seek_pos >= 0) {
		double ret = blend_input(0, cur_seek_pos, true, true, 1.0, FILTER_IGNORE, true, p_test_only);
		set_parameter(seek_pos_request, -1.0); 
		return ret;
	} else {
		return blend_input(0, p_time, false, p_is_external_seeking, 1.0, FILTER_IGNORE, true, p_test_only);
	}
}
void AnimationNodeTimeSeek::_bind_methods() {