### 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)

Ref<AnimationNode> ret;
	GDVIRTUAL_CALL(_get_child_by_name, p_name, ret);
	return ret;
}
Ref<AnimationNode> AnimationNode::find_node_by_path(const String &p_name) const {
	Vector<String> split = p_name.split("/");
	Ref<AnimationNode> ret = const_cast<AnimationNode *>(this);
	for (int i = 0; i < split.size(); i++) {
		ret = ret->get_child_by_name(split[i]);
		if (!ret.is_valid()) {
			break;
		}
	}
	return ret;
}
void AnimationNode::blend_animation_ex(const StringName &p_animation, double p_time, double p_delta, bool p_seeked, bool p_is_external_seeking, real_t p_blend, Animation::LoopedFlag p_looped_flag) {
	AnimationMixer::PlaybackInfo info;
	info.time = p_time;
	info.delta = p_delta;
	info.seeked = p_seeked;
	info.is_external_seeking = p_is_external_seeking;
	info.weight = p_blend;
	info.looped_flag = p_looped_flag;
	blend_animation(p_animation, info);
}
double AnimationNode::blend_node_ex(const StringName &p_sub_path, Ref<AnimationNode> p_node, double p_time, bool p_seek, bool p_is_external_seeking, real_t p_blend, FilterAction p_filter, bool p_sync, bool p_test_only) {