### 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)

return closable;
}
bool AnimationNode::is_path_filtered(const NodePath &p_path) const {
	return filter.has(p_path);
}
bool AnimationNode::has_filter() const {
	bool ret = false;
	GDVIRTUAL_CALL(_has_filter, ret);
	return ret;
}
Array AnimationNode::_get_filters() const {
	Array paths;
	for (const KeyValue<NodePath, bool> &E : filter) {
		paths.push_back(String(E.key)); // 
	}
	paths.sort(); // 
	return paths;
}
void AnimationNode::_set_filters(const Array &p_filters) {
	filter.clear();
	for (int i = 0; i < p_filters.size(); i++) {
		set_filter_path(p_filters[i], true);
	}
}
void AnimationNode::_validate_property(PropertyInfo &p_property) const {
	if (!has_filter() && (p_property.name == "filter_enabled" || p_property.name == "filters")) {
		p_property.usage = PROPERTY_USAGE_NONE;
	}
}
Ref<AnimationNode> AnimationNode::get_child_by_name(const StringName &p_name) const {