### 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)

StringName travel = travel_request;
	travel_request = StringName();
	if (!playing) {
		_start(p_state_machine);
	}
	ERR_FAIL_COND_V(!p_state_machine->states.has(travel), false);
	ERR_FAIL_COND_V(!p_state_machine->states.has(current), false);
	if (current == travel) {
		return !p_is_allow_transition_to_self;
	}
	Vector<StringName> new_path;
	Vector2 current_pos = p_state_machine->states[current].position;
	Vector2 target_pos = p_state_machine->states[travel].position;
	bool found_route = false;
	HashMap<StringName, AStarCost> cost_map;
	List<int> open_list;
	
	for (int i = 0; i < p_state_machine->transitions.size(); i++) {
		if (p_state_machine->transitions[i].transition->get_advance_mode() == AnimationNodeStateMachineTransition::ADVANCE_MODE_DISABLED) {
			continue;
		}
		if (p_state_machine->transitions[i].from == current) {
			open_list.push_back(i);
			float cost = p_state_machine->states[p_state_machine->transitions[i].to].position.distance_to(current_pos);
			cost *= p_state_machine->transitions[i].transition->get_priority();