As @AllanBenvin_yyc said in https://community.esri.com/t5/data-management-questions/move-feature-classes-out-of-feature-dataset/...:
…I am also hoping for a way to be able to move, not copy layers in/out of an FDS using arcpy. All the posts I have found refer to making a copy. This isn't feasible in our situation as it plays havoc with relationship classes, domains, archives etc. In the past we had to write a little ArcMap SDK executable that would do this. Since we have things like attribute rules now this won't work. An arcpy solution would be the best.