### Godot version

4.2

### System information

Linux

### Issue description

A nested state machine isn't traveling to its animation in `_ready()` in 4.2 as it was in 4.1.3.

In the ready function, we make the `root` state machine travel to the state of the `Stages` nested state machine. Then we immediately call the `Stages` nested state machine to travel to `Stage2`. This works fine in Godot v4.1.3, but not in Godot v4.2, where it seems a delay is first needed for the second travel animation to work.

![image](https://github.com/godotengine/godot/assets/788630/f1582a99-a68e-45d9-82b8-8367e62a9cba)
![image](https://github.com/godotengine/godot/assets/788630/c7c1f9fa-c78b-4259-bd36-81ebd8cef9aa)

### Steps to reproduce

Run the MRP below in 4.1.3 and 4.2.

In 4.1.3, the animation tree will reach `Stage2` and show Finished on the screen.

In 4.2, the animation tree will only reach `Stage1` and show Stuck on the screen.

### Minimal reproduction project

[MRP-AnimationNodeStateMachinePlayback.zip](https://github.com/godotengine/godot/files/13533132/MRP-AnimationNodeStateMachinePlayback.zip)

ERR_FAIL_COND_V_EDMSG(!states.has(p_name), Ref<AnimationNode>(), String(p_name) + " is not found current state.");
	return states[p_name].node;
}
StringName AnimationNodeStateMachine::get_node_name(const Ref<AnimationNode> &p_node) const {
	for (const KeyValue<StringName, State> &E : states) {
		if (E.value.node == p_node) {
			return E.key;
		}
	}
	ERR_FAIL_V(StringName());
}
void AnimationNodeStateMachine::get_child_nodes(List<ChildNode> *r_child_nodes) {
	Vector<StringName> nodes;
	for (const KeyValue<StringName, State> &E : states) {
		nodes.push_back(E.key);
	}
	nodes.sort_custom<StringName::AlphCompare>();
	for (int i = 0; i < nodes.size(); i++) {
		ChildNode cn;
		cn.name = nodes[i];
		cn.node = states[cn.name].node;
		r_child_nodes->push_back(cn);
	}
}
bool AnimationNodeStateMachine::has_node(const StringName &p_name) const {