### 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)

state_machine_type = p_state_machine_type;
	emit_changed();
	emit_signal(SNAME("tree_changed"));
	notify_property_list_changed();
}
AnimationNodeStateMachine::StateMachineType AnimationNodeStateMachine::get_state_machine_type() const {
	return state_machine_type;
}
void AnimationNodeStateMachine::set_allow_transition_to_self(bool p_enable) {
	allow_transition_to_self = p_enable;
}
bool AnimationNodeStateMachine::is_allow_transition_to_self() const {
	return allow_transition_to_self;
}
void AnimationNodeStateMachine::set_reset_ends(bool p_enable) {
	reset_ends = p_enable;
}
bool AnimationNodeStateMachine::are_ends_reset() const {
	return reset_ends;
}
bool AnimationNodeStateMachine::can_edit_node(const StringName &p_name) const {
	if (states.has(p_name)) {
		return !(states[p_name].node->is_class("AnimationNodeStartState") || states[p_name].node->is_class("AnimationNodeEndState"));
	}
	return true;
}
Ref<AnimationNode> AnimationNodeStateMachine::get_node(const StringName &p_name) const {