What is this kanji in Kaguya-sama's anime?
The kanji on the fan that was given by Kaguya is 磨穿鉄硯【ませんてっけん】.

According to weblio, the translation is correct:


  showing unyielding diligence in one's studies; wearing a hole through one's metal inkstone from constant studying


This is actually a yojijukugo or "four-character idiom" that is easier to search compared to identifying the characters in Japanese calligraphy directly.