FWIW my school introduced e as a base of natural logarithms with “it’s a special number, don’t worry about it. Good thing: your calculator knows them, too” and for a while we all thought that “natural” somehow related to being calculator-friendly.

Then later we got introduction to e in terms of derivatives and complex numbers. However, compound interest was never used for exploration, and I only got introduced to the it’s connection to e and as an explanation for what e is late in my thirties.