### 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)

ERR_FAIL_COND_V_MSG(group_start_transition.is_null(), Ref<AnimationNodeStateMachineTransition>(), "Group start transition is null.");
	return group_start_transition;
}
Ref<AnimationNodeStateMachineTransition> AnimationNodeStateMachinePlayback::_get_group_end_transition() const {
	ERR_FAIL_COND_V_MSG(group_end_transition.is_null(), Ref<AnimationNodeStateMachineTransition>(), "Group end transition is null.");
	return group_end_transition;
}
void AnimationNodeStateMachinePlayback::_bind_methods() {
	ClassDB::bind_method(D_METHOD("travel", "to_node", "reset_on_teleport"), &AnimationNodeStateMachinePlayback::travel, DEFVAL(true));
	ClassDB::bind_method(D_METHOD("start", "node", "reset"), &AnimationNodeStateMachinePlayback::start, DEFVAL(true));
	ClassDB::bind_method(D_METHOD("next"), &AnimationNodeStateMachinePlayback::next);
	ClassDB::bind_method(D_METHOD("stop"), &AnimationNodeStateMachinePlayback::stop);
	ClassDB::bind_method(D_METHOD("is_playing"), &AnimationNodeStateMachinePlayback::is_playing);
	ClassDB::bind_method(D_METHOD("get_current_node"), &AnimationNodeStateMachinePlayback::get_current_node);
	ClassDB::bind_method(D_METHOD("get_current_play_position"), &AnimationNodeStateMachinePlayback::get_current_play_pos);
	ClassDB::bind_method(D_METHOD("get_current_length"), &AnimationNodeStateMachinePlayback::get_current_length);
	ClassDB::bind_method(D_METHOD("get_fading_from_node"), &AnimationNodeStateMachinePlayback::get_fading_from_node);
	ClassDB::bind_method(D_METHOD("get_travel_path"), &AnimationNodeStateMachinePlayback::_get_travel_path);
}
AnimationNodeStateMachinePlayback::AnimationNodeStateMachinePlayback() {