Joseph Sisko’s restaurant is his personal property, not his private property since it is not a money-making venture. Since money, and capitalism, do not exist in the Federation, there is no private property in any form. Furthermore, given Star Trek’s egalitarian/utopian vision of the future, no one is going to take Joseph Sisko’s restaurant – the laws of the United Earth government (which has direct jurisdiction over Earth) exist (imo) to protect people’s personal property, not take it away.