Sorry to nitpick but the things that HACS provides are not add-ons. Everything in HACS is an integration, frontend thing or things like AppDaemon Apps or Python scripts.
People are always confused about that distinction. And so much so that the author of HACS baked in an acknowledgement when you install HACS that it doesn’t provide Add-Ons - at all.
that said I’m not aware of any service call that can reload an integration directly.
there is this service call:
homeassistant.reload_config_entry
but you’ll need to do some work to find the info for that integration.
Or I think you might be able to just use an entity_id that is provided by that integration and it reloads the integration.
see this thread: