### 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)

#include "animation_tree.h"
#include "animation_tree.compat.inc"
#include "animation_blend_tree.h"
#include "core/config/engine.h"
#include "scene/scene_string_names.h"
void AnimationNode::get_parameter_list(List<PropertyInfo> *r_list) const {
	Array parameters;
	if (GDVIRTUAL_CALL(_get_parameter_list, parameters)) {
		for (int i = 0; i < parameters.size(); i++) {
			Dictionary d = parameters[i];
			ERR_CONTINUE(d.is_empty());
			r_list->push_back(PropertyInfo::from_dict(d));
		}
	}
}
Variant AnimationNode::get_parameter_default_value(const StringName &p_parameter) const {
	Variant ret;
	GDVIRTUAL_CALL(_get_parameter_default_value, p_parameter, ret);
	return ret;
}
bool AnimationNode::is_parameter_read_only(const StringName &p_parameter) const {
	bool ret = false;
	GDVIRTUAL_CALL(_is_parameter_read_only, p_parameter, ret);
	return ret;
}
void AnimationNode::set_parameter(const StringName &p_name, const Variant &p_value) {