I have always thought that "neo" meant "new" in this context. It acknowledges that government is responsible for the non-wealthy via policy, but that the best way to assure their well being is via the market. If you scratch the surface of most of Biden's policies you'll find that they shovel new money creation to unnecessary corporate entities in the private sector, such as Obamacare and the windfall it provides to insurance. Obama and Biden were classic neoliberals that have the approval of the oligarchy if they can't instal a neocon.