Is it permissible to use a drawing tablet that erases with the push of a button to write on it for the sole purpose of memorization, without observing writing style, diacritics, or word accuracy?

There is no harm in using this method of writing the Holy Quran to memorize it. Adhering to the Uthmani script is required when writing Mushafs (copies of the Quran), but it is not necessary when writing some verses for citation.