### 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.

for (const KeyValue<StringName, Node> &E : nodes) {
		if (E.value.node == p_node) {
			return E.key;
		}
	}
	ERR_FAIL_V(StringName());
}
void AnimationNodeBlendTree::set_node_position(const StringName &p_node, const Vector2 &p_position) {
	ERR_FAIL_COND(!nodes.has(p_node));
	nodes[p_node].position = p_position;
}
Vector2 AnimationNodeBlendTree::get_node_position(const StringName &p_node) const {
	ERR_FAIL_COND_V(!nodes.has(p_node), Vector2());
	return nodes[p_node].position;
}
void AnimationNodeBlendTree::get_child_nodes(List<ChildNode> *r_child_nodes) {
	Vector<StringName> ns;
	for (const KeyValue<StringName, Node> &E : nodes) {
		ns.push_back(E.key);
	}
	for (int i = 0; i < ns.size(); i++) {
		ChildNode cn;
		cn.name = ns[i];
		cn.node = nodes[cn.name].node;
		r_child_nodes->push_back(cn);
	}
}
bool AnimationNodeBlendTree::has_node(const StringName &p_name) const {