### 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.

return "BlendTree";
}
double AnimationNodeBlendTree::_process(double p_time, bool p_seek, bool p_is_external_seeking, bool p_test_only) {
	Ref<AnimationNodeOutput> output = nodes[SceneStringNames::get_singleton()->output].node;
	return _blend_node("output", nodes[SceneStringNames::get_singleton()->output].connections, this, output, p_time, p_seek, p_is_external_seeking, 1.0, FILTER_IGNORE, true, nullptr, p_test_only);
}
void AnimationNodeBlendTree::get_node_list(List<StringName> *r_list) {
	for (const KeyValue<StringName, Node> &E : nodes) {
		r_list->push_back(E.key);
	}
}
void AnimationNodeBlendTree::set_graph_offset(const Vector2 &p_graph_offset) {
	graph_offset = p_graph_offset;
}
Vector2 AnimationNodeBlendTree::get_graph_offset() const {
	return graph_offset;
}
Ref<AnimationNode> AnimationNodeBlendTree::get_child_by_name(const StringName &p_name) const {
	return get_node(p_name);
}
bool AnimationNodeBlendTree::_set(const StringName &p_name, const Variant &p_value) {