### 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)

ERR_FAIL_INDEX_V(p_transition, transitions.size(), Ref<AnimationNodeStateMachineTransition>());
	return transitions[p_transition].transition;
}
StringName AnimationNodeStateMachine::get_transition_from(int p_transition) const {
	ERR_FAIL_INDEX_V(p_transition, transitions.size(), StringName());
	return transitions[p_transition].from;
}
StringName AnimationNodeStateMachine::get_transition_to(int p_transition) const {
	ERR_FAIL_INDEX_V(p_transition, transitions.size(), StringName());
	return transitions[p_transition].to;
}
bool AnimationNodeStateMachine::is_transition_across_group(int p_transition) const {
	ERR_FAIL_INDEX_V(p_transition, transitions.size(), false);
	if (get_state_machine_type() == AnimationNodeStateMachine::STATE_MACHINE_TYPE_GROUPED) {
		if (transitions[p_transition].from == "Start" || transitions[p_transition].to == "End") {
			return true;
		}
	}
	return false;
}
int AnimationNodeStateMachine::get_transition_count() const {