### 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 (start_request != StringName() || travel_request != StringName()) {
		if (p_state_machine->get_state_machine_type() != AnimationNodeStateMachine::STATE_MACHINE_TYPE_GROUPED) {
			_clear_path_children(tree, p_state_machine, p_test_only);
		}
	}
	if (start_request != StringName()) {
		path.clear();
		String start_target = _validate_path(p_state_machine, start_request);
		Vector<String> start_path = String(start_target).split("/");
		start_request = start_path[0];
		if (start_path.size()) {
			_start_children(tree, p_state_machine, start_target, p_test_only);
		}
		
		if (p_state_machine->states.has(start_request)) {
			_start(p_state_machine);
		} else {
			StringName node = start_request;
			ERR_FAIL_V_MSG(0, "No such node: '" + node + "'");
		}
	}
	if (travel_request != StringName()) {
		
		String travel_target = _validate_path(p_state_machine, travel_request);
		Vector<String> travel_path = travel_target.split("/");
		travel_request = travel_path[0];
		StringName temp_travel_request = travel_request;