### 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)

String prop_name = p_name;
	if (prop_name.begins_with("states/")) {
		String node_name = prop_name.get_slicec('/', 1);
		String what = prop_name.get_slicec('/', 2);
		if (what == "node") {
			Ref<AnimationNode> anode = p_value;
			if (anode.is_valid()) {
				add_node(node_name, p_value);
			}
			return true;
		}
		if (what == "position") {
			if (states.has(node_name)) {
				states[node_name].position = p_value;
			}
			return true;
		}
	} else if (prop_name == "transitions") {
		Array trans = p_value;
		ERR_FAIL_COND_V(trans.size() % 3 != 0, false);
		for (int i = 0; i < trans.size(); i += 3) {
			add_transition(trans[i], trans[i + 1], trans[i + 2]);
		}
		return true;
	} else if (prop_name == "graph_offset") {
		set_graph_offset(p_value);
		return true;
	}