### 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)

fading_from = StringName();
		fading_pos = 0;
		
		pos_current = 0; 
		pi.time = 0;
		pi.seeked = true;
		pi.is_external_seeking = false;
		pi.weight = 0;
		len_current = p_state_machine->blend_node(p_state_machine->states[current].node, current, pi, AnimationNode::FILTER_IGNORE, true, true);
		
		_transition_to_next_recursive(tree, p_state_machine, p_test_only);
	}
	
	if (!p_state_machine->states.has(current)) {
		playing = false; 
		_set_current(p_state_machine, StringName());
		return 0;
	}
	
	bool is_start_of_group = false;
	bool is_end_of_group = false;
	if (!p_state_machine->are_ends_reset() || p_state_machine->get_state_machine_type() == AnimationNodeStateMachine::STATE_MACHINE_TYPE_GROUPED) {
		is_start_of_group = fading_from == p_state_machine->start_node;
		is_end_of_group = current == p_state_machine->end_node;
	}
	
	float fade_blend = 1.0;
	if (fading_time && fading_from != StringName()) {
		if (!p_state_machine->states.has(fading_from)) {
			fading_from = StringName();