### 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)

} else {
		group_end_transition = Ref<AnimationNodeStateMachineTransition>();
	}
	
	if (anodesm->get_state_machine_type() == AnimationNodeStateMachine::STATE_MACHINE_TYPE_GROUPED) {
		indices = anodesm->find_transition_from(anodesm->start_node);
		int anodesm_start_size = indices.size();
		indices = anodesm->find_transition_to(anodesm->end_node);
		int anodesm_end_size = indices.size();
		if (group_start_size > 1) {
			WARN_PRINT_ED("There are two or more transitions to the Grouped AnimationNodeStateMachine in AnimationNodeStateMachine: " + base_path + ", which may result in unintended transitions.");
		}
		if (group_end_size > 1) {
			WARN_PRINT_ED("There are two or more transitions from the Grouped AnimationNodeStateMachine in AnimationNodeStateMachine: " + base_path + ", which may result in unintended transitions.");
		}
		if (anodesm_start_size > 1) {
			WARN_PRINT_ED("There are two or more transitions from the Start of Grouped AnimationNodeStateMachine in AnimationNodeStateMachine: " + base_path + current + ", which may result in unintended transitions.");
		}
		if (anodesm_end_size > 1) {
			WARN_PRINT_ED("There are two or more transitions to the End of Grouped AnimationNodeStateMachine in AnimationNodeStateMachine: " + base_path + current + ", which may result in unintended transitions.");
		}
		if (anodesm_start_size != group_start_size) {
			ERR_PRINT_ED("There is a mismatch in the number of start transitions in and out of the Grouped AnimationNodeStateMachine on AnimationNodeStateMachine: " + base_path + current + ".");
		}
		if (anodesm_end_size != group_end_size) {
			ERR_PRINT_ED("There is a mismatch in the number of end transitions in and out of the Grouped AnimationNodeStateMachine on AnimationNodeStateMachine: " + base_path + current + ".");
		}
	}
}
void AnimationNodeStateMachinePlayback::_set_grouped(bool p_is_grouped) {