Adult. I was married with a mortgage and two kids at that age. My 25 year old DD is a Staff Nurse in charge of wards. imo it's a little patronising not to consider someone to be fully grown and responsible by that age.
My son in law had served two tours of Afghanistan by 25. Young adult to me has connotations of ooh...barely out their teens. Not really a grown up.
It's not a term that should be still applicable in your mid twenties, surely?