### 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 = current;
			fading_time = next.xfade;
			fading_pos = 0;
		} else {
			if (reset_request) {
				
				pi.time = 0;
				pi.seeked = true;
				pi.is_external_seeking = false;
				pi.weight = 0;
				p_state_machine->blend_node(p_state_machine->states[current].node, current, pi, AnimationNode::FILTER_IGNORE, true, p_test_only);
			}
			fading_from = StringName();
			fading_time = 0;
			fading_pos = 0;
		}
		
		if (path.size()) {
			path.remove_at(0);
		}
		
		_set_current(p_state_machine, next.node);
		current_curve = next.curve;
		_reset_request_for_fading_from = reset_request; 
		reset_request = next.is_reset;
		pos_fade_from = pos_current;
		len_fade_from = len_current;
		if (next.switch_mode == AnimationNodeStateMachineTransition::SWITCH_MODE_SYNC) {
			pi.time = MIN(pos_current, len_current);
			pi.seeked = true;