While others might have been having more mainstream הערות or simply paying attention to the מגילה, I had the following observation:
ומה שאלתך וינתן לך ומה בקשתך עוד ותעש
Certainly, the word שאלה is feminine. Therefore, we would expect the פסוק to read ומה שאלתך ותנתן לך just as ותעש is in feminine form due to בקשה being feminine. I believe the following must be the explanation: If someone requests something, it is certainly possible to perform the request. However, if someone asks for something, you cannot give them "their asking." Rather, you give them the thing which they asked for. Therefore, we treat this as if there were a hidden word, perhaps as follows: ומה שאלתך וינתן הדבר לך and that is why it is masculine.
However, as MG points out in the comments, even בקשה switches seemingly to masculine earlier on in the מגילה. The אבן עזרא says there that it is referring to a hidden דבר. So my explanation for the gender change was correct. But my distinction between בקשה and שאלה apparently was not.