dritten != fourth

Die Übersetzung ist korrekt, weil die Stockwerke im deutschsprachigen Raum anders gezählt werden als in Japan und den Vereinigten Staaten. Was dort als „forth floor“ bzw. „４階“ bezeichnet wird, ist bei uns der dritte Stock oder das dritte Obergeschoß.

Yes, this set of translations is a bit of a mess and will be mostly unhelpful to a language learner because of different counting rules. In the English-speaking world, the "first floor" is synonymous with the ground-level floor, but what French speakers call "le premier étage" is the floor **above** the ground floor. Evidently German speakers maintain the same convention as the French. When the sentence is retranslated by someone unaware of this rule, we get the problem compounded, with various "equivalent" sentences using either the word for "third" or the word for "fourth."

If Wiktionary is correct, "first floor" means the floor **above** the ground floor in British English as well: https://en.wiktionary.org/wiki/first_floor

So it should be correct to also link #931434 "My flat is on the third floor."

It would be OK for a Brit to translate it as “third floor”, but “flat” usually means “Wohnung”. See #4113420. :-)