### 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)

for (int i = 0; i < transitions.size(); i++) {
		if (transitions[i].from == p_from) {
			return true;
		}
	}
	return false;
}
bool AnimationNodeStateMachine::has_transition_to(const StringName &p_to) const {
	for (int i = 0; i < transitions.size(); i++) {
		if (transitions[i].to == p_to) {
			return true;
		}
	}
	return false;
}
int AnimationNodeStateMachine::find_transition(const StringName &p_from, const StringName &p_to) const {
	for (int i = 0; i < transitions.size(); i++) {
		if (transitions[i].from == p_from && transitions[i].to == p_to) {
			return i;
		}
	}
	return -1;
}
Vector<int> AnimationNodeStateMachine::find_transition_from(const StringName &p_from) const {