### Godot version

4.2 RC2

### System information

Any

### Issue description

https://github.com/godotengine/godot/assets/61938263/42ed582f-7b87-424c-8d19-ba0650ead5aa

It should not be reset by pausing.

### Steps to reproduce

Pause AnimationPlaybackTrack

### Minimal reproduction project

N/A
List<StringName> to_erase;
	for (const KeyValue<StringName, AnimationData> &E : animation_set) {
		if (E.value.last_update != animation_set_update_pass) {
			
			to_erase.push_back(E.key);
			clear_cache_needed = true;
		}
	}
	while (to_erase.size()) {
		animation_set.erase(to_erase.front()->get());
		to_erase.pop_front();
	}
	if (clear_cache_needed) {
		
		_clear_caches();
	}
	emit_signal(SNAME("animation_list_changed"));
}
void AnimationMixer::_animation_added(const StringName &p_name, const StringName &p_library) {
	_animation_set_cache_update();
}
void AnimationMixer::_animation_removed(const StringName &p_name, const StringName &p_library) {
	StringName name = p_library == StringName() ? p_name : StringName(String(p_library) + "/" + String(p_name));
	if (!animation_set.has(name)) {
		return; 
	}
	_animation_set_cache_update();
	_remove_animation(name);
}
void AnimationMixer::_animation_renamed(const StringName &p_name, const StringName &p_to_name, const StringName &p_library) {