### 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 {
			pi.time = p_delta;
			root_animation_node->_pre_process(&process_state, pi);
		}
	}
	if (!process_state.valid) {
		return false; // 
	}
	return true;
}
void AnimationTree::_set_active(bool p_active) {
	_set_process(p_active);
	started = p_active;
}
void AnimationTree::set_advance_expression_base_node(const NodePath &p_path) {
	advance_expression_base_node = p_path;
}
NodePath AnimationTree::get_advance_expression_base_node() const {
	return advance_expression_base_node;
}
bool AnimationTree::is_state_invalid() const {
	return !process_state.valid;
}
String AnimationTree::get_invalid_state_reason() const {
	return process_state.invalid_reasons;
}
uint64_t AnimationTree::get_last_process_pass() const {
	return process_pass;
}
PackedStringArray AnimationTree::get_configuration_warnings() const {