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Not a native English here and I'm having the issue with I didn't and I haven't use when saying
I hope I didn't forget/haven't forgotten anything
(to say/mention when answering the email or message) at the end of the email/message/letter.
Can you please help me understand this in the easiest possible way.
In the general case, the two mean the same thing, but as noted here, did should reference something that happened in the past, whereas have should reference something in the past that may still have impact or relevance today.
But if you're just worried about the case "I hope I didn't forget / haven't forgotten anything", they are both perfectly grammatically correct in the context, though "didn't forget" could be interpreted as slightly less formal, and more close to spoken language whereas "haven't forgotten" could be seen as more formal and more suited for written language.
