### 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)

emit_signal(SNAME("tree_changed"));
}
void AnimationRootNode::_animation_node_renamed(const ObjectID &p_oid, const String &p_old_name, const String &p_new_name) {
	emit_signal(SNAME("animation_node_renamed"), p_oid, p_old_name, p_new_name);
}
void AnimationRootNode::_animation_node_removed(const ObjectID &p_oid, const StringName &p_node) {
	emit_signal(SNAME("animation_node_removed"), p_oid, p_node);
}
//
void AnimationTree::set_root_animation_node(const Ref<AnimationRootNode> &p_animation_node) {
	if (root_animation_node.is_valid()) {
		root_animation_node->disconnect(SNAME("tree_changed"), callable_mp(this, &AnimationTree::_tree_changed));
		root_animation_node->disconnect(SNAME("animation_node_renamed"), callable_mp(this, &AnimationTree::_animation_node_renamed));
		root_animation_node->disconnect(SNAME("animation_node_removed"), callable_mp(this, &AnimationTree::_animation_node_removed));
	}
	root_animation_node = p_animation_node;
	if (root_animation_node.is_valid()) {
		root_animation_node->connect(SNAME("tree_changed"), callable_mp(this, &AnimationTree::_tree_changed));
		root_animation_node->connect(SNAME("animation_node_renamed"), callable_mp(this, &AnimationTree::_animation_node_renamed));
		root_animation_node->connect(SNAME("animation_node_removed"), callable_mp(this, &AnimationTree::_animation_node_removed));
	}
	properties_dirty = true;
	update_configuration_warnings();
}
Ref<AnimationRootNode> AnimationTree::get_root_animation_node() const {
	return root_animation_node;
}
bool AnimationTree::_blend_pre_process(double p_delta, int p_track_count, const HashMap<NodePath, int> &p_track_map) {