### 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)

if (base_path.is_empty()) {
		return Ref<AnimationNodeStateMachine>();
	}
	Vector<String> split = base_path.split("/");
	ERR_FAIL_COND_V_MSG(split.size() < 3, Ref<AnimationNodeStateMachine>(), "Path is too short.");
	split = split.slice(1, split.size() - 2);
	Ref<AnimationNode> root = p_tree->get_root_animation_node();
	ERR_FAIL_COND_V_MSG(root.is_null(), Ref<AnimationNodeStateMachine>(), "There is no root AnimationNode in AnimationTree: " + String(p_tree->get_name()));
	String anodesm_path = String("/").join(split);
	Ref<AnimationNodeStateMachine> anodesm = !anodesm_path.size() ? root : root->find_node_by_path(anodesm_path);
	ERR_FAIL_COND_V_MSG(anodesm.is_null(), Ref<AnimationNodeStateMachine>(), "Can't get state machine with path: " + anodesm_path);
	return anodesm;
}
Ref<AnimationNodeStateMachineTransition> AnimationNodeStateMachinePlayback::_get_group_start_transition() const {