Every cruise I’ve ever been in (Norwegian, Royal Caribbean, Celebrity) have had both standard American 110v and continental Europe outlets. I know several times my parents have used adapters to utilize more outlets and never had them confiscated. I’ve never tried to bring an extension cord or power strip on board.
Ive heard the ban on power strips has something to do with how built in surge protectors (often in power strips) operate and the unstable characteristics of boats power systems risking the surge protectors catching on fire. I’d imagine power draw might be another concern for the ships.