This is a late reply, but just to confirm: the apartments are per ward (including subdivisions) and not one per country. This is confirmed by Yoshida during the recent Letter from the Producer at around 2:09:20 in the Twitch stream, and is also mentioned on the 4gamer summary of the stream which states:

このアパルトメントは，3国の冒険者居住区の各区画に1棟ずつ建ち，部屋の代金は50万ギルになるという。

The Japanese ff14wiki also clarifies:

ハウジングエリアの区画1つにつき、一棟。拡張エリアにも立つ。1棟あたり512戸。 12区＋拡張エリア＝24区。24区×三国＝72区。72×512戸＝1ワールドあたり36,864戸ということになる。

Yoshida also mentioned on the live stream that, if it wasn't enough, they could still add more (but I tend to think this will be enough for all but the absolute busiest of servers, at least for now).