Acipenser brevirostrum and sturio are appendix I, which you cannot own without a Captive bred wildlife permit and captive bred animal.
All other Aciepensiformes spp. are listed in CITES appendix II which would have to be captive bred to be legally sold. So just about all the ones bought and sold commercially are captive bred and legal to own. Unless you caught it yourself in the wild.
There are no wild caught sturgeons being sold as pets. Many species are now cultivated for food and for caviar. So keeping them for a pet is not endangering any wild population.