### 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)

child_info.is_reset = is_deepest_state ? reset_request_on_teleport : false;
			playback->_travel_main(temp_path[i], child_info.is_reset);
			if (playback->_make_travel_path(p_tree, anodesm.ptr(), is_deepest_state ? p_is_allow_transition_to_self : false, child_info.path, p_test_only)) {
				found_route &= child_found_route;
			} else {
				child_info.path.push_back(temp_path[i]);
				found_route = false;
			}
			children.push_back(child_info);
		}
		reset_request_on_teleport = false;
	}
	if (found_route) {
		for (int i = 0; i < children.size(); i++) {
			children.write[i].playback->clear_path();
			for (int j = 0; j < children[i].path.size(); j++) {
				children.write[i].playback->push_path(children[i].path[j]);
			}
		}
	} else {
		for (int i = 0; i < children.size(); i++) {
			children.write[i].playback->_travel_main(StringName(), children[i].is_reset); 
			if (children[i].path.size()) {
				children.write[i].playback->_start_main(children[i].path[children[i].path.size() - 1], children[i].is_reset);
			}
		}
	}
	return found_route;
}
void AnimationNodeStateMachinePlayback::_start(AnimationNodeStateMachine *p_state_machine) {