### 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)

if (p_parameter == playback) {
		Ref<AnimationNodeStateMachinePlayback> p;
		p.instantiate();
		return p;
	} else {
		return false; 
	}
}
bool AnimationNodeStateMachine::is_parameter_read_only(const StringName &p_parameter) const {
	if (p_parameter == playback) {
		return true;
	}
	return false;
}
void AnimationNodeStateMachine::add_node(const StringName &p_name, Ref<AnimationNode> p_node, const Vector2 &p_position) {
	ERR_FAIL_COND(states.has(p_name));
	ERR_FAIL_COND(p_node.is_null());
	ERR_FAIL_COND(String(p_name).contains("/"));
	State state_new;
	state_new.node = p_node;
	state_new.position = p_position;
	states[p_name] = state_new;
	emit_changed();
	emit_signal(SNAME("tree_changed"));
	p_node->connect("tree_changed", callable_mp(this, &AnimationNodeStateMachine::_tree_changed), CONNECT_REFERENCE_COUNTED);
	p_node->connect("animation_node_renamed", callable_mp(this, &AnimationNodeStateMachine::_animation_node_renamed), CONNECT_REFERENCE_COUNTED);
	p_node->connect("animation_node_removed", callable_mp(this, &AnimationNodeStateMachine::_animation_node_removed), CONNECT_REFERENCE_COUNTED);
}
void AnimationNodeStateMachine::replace_node(const StringName &p_name, Ref<AnimationNode> p_node) {