### 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)

AStarCost ap;
			ap.prev = current;
			ap.distance = cost;
			cost_map[p_state_machine->transitions[i].to] = ap;
			if (p_state_machine->transitions[i].to == travel) { 
				found_route = true;
				break;
			}
		}
	}
	
	while (!found_route) {
		if (open_list.size() == 0) {
			break; 
		}
		
		List<int>::Element *least_cost_transition = nullptr;
		float least_cost = 1e20;
		for (List<int>::Element *E = open_list.front(); E; E = E->next()) {
			float cost = cost_map[p_state_machine->transitions[E->get()].to].distance;
			cost += p_state_machine->states[p_state_machine->transitions[E->get()].to].position.distance_to(target_pos);
			if (cost < least_cost) {
				least_cost_transition = E;
				least_cost = cost;
			}
		}
		StringName transition_prev = p_state_machine->transitions[least_cost_transition->get()].from;
		StringName transition = p_state_machine->transitions[least_cost_transition->get()].to;
		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) {