### 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)

_set_base_path(p_base_path);
	AnimationTree *tree = p_state_machine->process_state->tree;
	double p_time = p_playback_info.time;
	bool p_seek = p_playback_info.seeked;
	bool p_is_external_seeking = p_playback_info.is_external_seeking;
	
	if (p_time == 0 && p_seek && !p_is_external_seeking) {
		if (p_state_machine->state_machine_type != AnimationNodeStateMachine::STATE_MACHINE_TYPE_NESTED || is_end() || !playing) {
			
			if (p_state_machine->get_state_machine_type() != AnimationNodeStateMachine::STATE_MACHINE_TYPE_GROUPED) {
				path.clear();
				_clear_path_children(tree, p_state_machine, p_test_only);
				_start(p_state_machine);
			}
			reset_request = true;
		} else {
			
			reset_request = true;
			teleport_request = true;
		}
	}
	if (stop_request) {
		start_request = StringName();
		travel_request = StringName();
		path.clear();
		playing = false;
		return 0;
	}
	if (!playing && start_request != StringName() && travel_request != StringName()) {
		return 0;