### 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.

if (p_parameter == active || p_parameter == internal_active) {
		return true;
	}
	return false;
}
void AnimationNodeOneShot::set_fade_in_time(double p_time) {
	fade_in = p_time;
}
double AnimationNodeOneShot::get_fade_in_time() const {
	return fade_in;
}
void AnimationNodeOneShot::set_fade_out_time(double p_time) {
	fade_out = p_time;
}
double AnimationNodeOneShot::get_fade_out_time() const {
	return fade_out;
}
void AnimationNodeOneShot::set_fade_in_curve(const Ref<Curve> &p_curve) {
	fade_in_curve = p_curve;
}
Ref<Curve> AnimationNodeOneShot::get_fade_in_curve() const {
	return fade_in_curve;
}
void AnimationNodeOneShot::set_fade_out_curve(const Ref<Curve> &p_curve) {
	fade_out_curve = p_curve;
}
Ref<Curve> AnimationNodeOneShot::get_fade_out_curve() const {
	return fade_out_curve;
}
void AnimationNodeOneShot::set_auto_restart_enabled(bool p_enabled) {