They stopped hiring for the position I was interested in because they already had a sufficient number of applicants.
They are no longer accepting applications for the position I was interested in because they have already received enough applications.
英語は日本語ほどへりくだりはないのですが、解答1も解答２もフォーマルな言い方です。もっとカジュアルで言いますと “They aren’t hiring for the job I was interested in anymore because they already got enough people.” “position” も “job” も仕事の事ですが、 “position” の方がフォーマルな言い方です。 “have” も “got” よりフォーマルになります。
The position you were interested in has been closed as it has been filled.
The position you were interested in has been closed as it has been filled.
Unfortunately, recruitment for the position has been closed due to the position being filled.
We regret to inform you that the position has already been filled.
「興味があった求人は充足の為募集を締切りました」は英語では、
the position has been filled
「そのポジションは充足した」
recruitment has been closed
「募集を締め切った」
という表現を使うのが自然です。
アメリカ合衆国 
