### 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_changed();
	AnimationRootNode::_tree_changed();
}
void AnimationNodeStateMachine::_animation_node_renamed(const ObjectID &p_oid, const String &p_old_name, const String &p_new_name) {
	AnimationRootNode::_animation_node_renamed(p_oid, p_old_name, p_new_name);
}
void AnimationNodeStateMachine::_animation_node_removed(const ObjectID &p_oid, const StringName &p_node) {
	AnimationRootNode::_animation_node_removed(p_oid, p_node);
}
void AnimationNodeStateMachine::_bind_methods() {
	ClassDB::bind_method(D_METHOD("add_node", "name", "node", "position"), &AnimationNodeStateMachine::add_node, DEFVAL(Vector2()));
	ClassDB::bind_method(D_METHOD("replace_node", "name", "node"), &AnimationNodeStateMachine::replace_node);
	ClassDB::bind_method(D_METHOD("get_node", "name"), &AnimationNodeStateMachine::get_node);
	ClassDB::bind_method(D_METHOD("remove_node", "name"), &AnimationNodeStateMachine::remove_node);
	ClassDB::bind_method(D_METHOD("rename_node", "name", "new_name"), &AnimationNodeStateMachine::rename_node);
	ClassDB::bind_method(D_METHOD("has_node", "name"), &AnimationNodeStateMachine::has_node);
	ClassDB::bind_method(D_METHOD("get_node_name", "node"), &AnimationNodeStateMachine::get_node_name);
	ClassDB::bind_method(D_METHOD("set_node_position", "name", "position"), &AnimationNodeStateMachine::set_node_position);
	ClassDB::bind_method(D_METHOD("get_node_position", "name"), &AnimationNodeStateMachine::get_node_position);
	ClassDB::bind_method(D_METHOD("has_transition", "from", "to"), &AnimationNodeStateMachine::has_transition);
	ClassDB::bind_method(D_METHOD("add_transition", "from", "to", "transition"), &AnimationNodeStateMachine::add_transition);
	ClassDB::bind_method(D_METHOD("get_transition", "idx"), &AnimationNodeStateMachine::get_transition);
	ClassDB::bind_method(D_METHOD("get_transition_from", "idx"), &AnimationNodeStateMachine::get_transition_from);
	ClassDB::bind_method(D_METHOD("get_transition_to", "idx"), &AnimationNodeStateMachine::get_transition_to);
	ClassDB::bind_method(D_METHOD("get_transition_count"), &AnimationNodeStateMachine::get_transition_count);
	ClassDB::bind_method(D_METHOD("remove_transition_by_index", "idx"), &AnimationNodeStateMachine::remove_transition_by_index);
	ClassDB::bind_method(D_METHOD("remove_transition", "from", "to"), &AnimationNodeStateMachine::remove_transition);