### 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)

Vector<StringName> new_path;
		bool can_travel = _make_travel_path(tree, p_state_machine, travel_path.size() <= 1 ? p_state_machine->is_allow_transition_to_self() : false, new_path, p_test_only);
		if (travel_path.size()) {
			if (can_travel) {
				can_travel = _travel_children(tree, p_state_machine, travel_target, p_state_machine->is_allow_transition_to_self(), travel_path[0] == current, p_test_only);
			} else {
				_start_children(tree, p_state_machine, travel_target, p_test_only);
			}
		}
		
		if (can_travel) {
			path = new_path;
		} else {
			
			if (p_state_machine->states.has(temp_travel_request)) {
				path.clear();
				if (current != temp_travel_request || reset_request_on_teleport) {
					_set_current(p_state_machine, temp_travel_request);
					reset_request = reset_request_on_teleport;
					teleport_request = true;
				}
			} else {
				ERR_FAIL_V_MSG(0, "No such node: '" + temp_travel_request + "'");
			}
		}
	}
	AnimationMixer::PlaybackInfo pi = p_playback_info;
	if (teleport_request) {
		teleport_request = false;