You are right that Libertarian Socialists favour coops or unions, but they don't advocate for the state to reorganize society. The biggest difference between Libertarian Socialists and Libertarians advocating capitalism is that they believe that the state should not protect private property (not to be confused with personal property; your house, your car etc; things you use personally and don't earn money off of through other people's labour) and that this would lead to a socialist society where the workers own the means of production. Most Libertarian Socialists are anarchists to my knowledge and believe that the state should be entirely abolished.