Mayo vs vinegar is kind of an actual debate in germany. The civilised side and the vinegar people are mostly blissfully unaware of each other until they develop righteous hatred for the other salad as soon as they learn of it. I heard the vinegar version is eaten warm, which sounds even worse. I would say both are authentic, but vinegar potato salad is authentically horrible.
Storebought potato salad will also at best get people talking behind your back in germany, no matter which kind.