-「に」：Point of action, Target place of action. where you do to.Concentration Point. * 勉強に、いそしむ／集中する／励む -「で」＝「に」＋「て」：Where you do. Platform of your action. 　＊ 勉強で、忙しい／大変だ／人生変わった ※「て」：a particle adding the implication of finish/fix, in terms of aspect -------------------------------------------------- - in XXX に忙しい and XXX で忙しい, 「に」＆「で」 are usually interexchangeabele. Using either of them, the sentence would make sense. - Personally, I would use 「で」

I think that this difference is too small and slight for even Japanese people to explain perfectly. In almost all situations, you can use them interchangebly. Therefore, regarding the example above, whichever has the same meaning. But If I dare to say the difference, で忙しい can be used more generally. There may be few cases where "に忙しい" sound a little bit weird. I think this is because "で忙しい” basically put more focus on the reason why a person is busy. That's why, if you are asked about the reason why you are busy, it may sound more natural if you answer "～で忙しい". But "に忙しい” is not wrong. Anyway, this difference is toooo small. At least I think there would be no problem if you think that these are the same. I hope my answer would be any help to you.

〇〇に忙しいとは言いません。基本的に〇〇で忙しいと言います[emoji]