Jisho

Because 初め and 初めて are two different words that don't come from a baseline conjugation (for instance, using 初める with that kanji isn't done). If you could write 初める, then you'd just have one entry, which would be はじ.める for the kun'yomi, but since that's not possible, they have to show that both はじ.め and はじ.めて are possible, since those are separate words.

Japanese-language kanji dictionaries break them down in the same way.

https://www.kanjipedia.jp/kanji/0003275800

Kanjipedia does not share the same data resources as jisho.

I guess I couldn't explain what I wanted to say.

As you can see from the image(https://prnt.sc/101u6l0), there are two "exactly same" explanations. It doesn't make sense.

You're right about the grammer thing but it is not for what I meant to say.

Ah, I don't think I've ever even looked at that part of the kanji info screen before. My bad.