### 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)

AnimationMixer::PlaybackInfo info;
	info.time = p_time;
	info.seeked = p_seek;
	info.is_external_seeking = p_is_external_seeking;
	info.weight = p_blend;
	return blend_node(p_node, p_sub_path, info, p_filter, p_sync, p_test_only);
}
double AnimationNode::blend_input_ex(int p_input, double p_time, bool p_seek, bool p_is_external_seeking, real_t p_blend, FilterAction p_filter, bool p_sync, bool p_test_only) {
	AnimationMixer::PlaybackInfo info;
	info.time = p_time;
	info.seeked = p_seek;
	info.is_external_seeking = p_is_external_seeking;
	info.weight = p_blend;
	return blend_input(p_input, info, p_filter, p_sync, p_test_only);
}
void AnimationNode::_bind_methods() {
	ClassDB::bind_method(D_METHOD("add_input", "name"), &AnimationNode::add_input);
	ClassDB::bind_method(D_METHOD("remove_input", "index"), &AnimationNode::remove_input);
	ClassDB::bind_method(D_METHOD("set_input_name", "input", "name"), &AnimationNode::set_input_name);
	ClassDB::bind_method(D_METHOD("get_input_name", "input"), &AnimationNode::get_input_name);
	ClassDB::bind_method(D_METHOD("get_input_count"), &AnimationNode::get_input_count);
	ClassDB::bind_method(D_METHOD("find_input", "name"), &AnimationNode::find_input);
	ClassDB::bind_method(D_METHOD("set_filter_path", "path", "enable"), &AnimationNode::set_filter_path);
	ClassDB::bind_method(D_METHOD("is_path_filtered", "path"), &AnimationNode::is_path_filtered);
	ClassDB::bind_method(D_METHOD("set_filter_enabled", "enable"), &AnimationNode::set_filter_enabled);