### 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)

ERR_FAIL_NULL(process_state);
	if (process_state->is_testing) {
		return;
	}
	ERR_FAIL_COND(!process_state->tree->property_parent_map.has(node_state.base_path));
	ERR_FAIL_COND(!process_state->tree->property_parent_map[node_state.base_path].has(p_name));
	StringName path = process_state->tree->property_parent_map[node_state.base_path][p_name];
	process_state->tree->property_map[path].first = p_value;
}
Variant AnimationNode::get_parameter(const StringName &p_name) const {
	ERR_FAIL_NULL_V(process_state, Variant());
	ERR_FAIL_COND_V(!process_state->tree->property_parent_map.has(node_state.base_path), Variant());
	ERR_FAIL_COND_V(!process_state->tree->property_parent_map[node_state.base_path].has(p_name), Variant());
	StringName path = process_state->tree->property_parent_map[node_state.base_path][p_name];
	return process_state->tree->property_map[path].first;
}
void AnimationNode::get_child_nodes(List<ChildNode> *r_child_nodes) {
	Dictionary cn;
	if (GDVIRTUAL_CALL(_get_child_nodes, cn)) {
		List<Variant> keys;
		cn.get_key_list(&keys);
		for (const Variant &E : keys) {
			ChildNode child;
			child.name = E;
			child.node = cn[E];
			r_child_nodes->push_back(child);
		}
	}
}
void AnimationNode::blend_animation(const StringName &p_animation, AnimationMixer::PlaybackInfo p_playback_info) {