Is writing an expository paper helpful for math PhD admission?

An expository paper is useful in the abstract, but how much it will actually help you depends on the circumstances.

The basic problem is that if you hand a random mathematician an expository paper on microlocal sheaf theory, they won't know what to make of it. Is it even correct? Is it plagiarized? Is it completely routine (closely following standard sources), or does it show creativity in the organization or explanations? Unless the reader has real expertise, they won't be able to judge it without a lot of time and effort, and there's a real chance that nobody on the admissions committee will have that expertise. If everything goes well, they'll forward your paper to an expert who will give them an informed judgment. But if that expert turns out to be busy or disorganized, your paper may fall through the cracks and end up not counting for much with the admissions committee.

You can get around this by making sure at least one of your letters of recommendation discusses the paper. If the recommender can vouch for the quality and originality of the paper, then that will mean a lot. Of course this means you have to convince someone to take a serious look at it, but your chances of doing this are at least as high as the admissions committee's.

If you are writing the paper under the supervision of a faculty member who is happy to read it and write a letter of recommendation, then that's great. I'm not sure I'd recommend just writing one on your own, however. It could work out well, but there's a risk of not getting much admissions benefit from it, so this would make sense only if you feel writing the paper would be a rewarding activity even aside from graduate admissions.

If you've already given talks that will be discussed in your letters, then that could be good enough. An expository paper comes across as more serious and convincing than just some talks, but not necessarily enough so to justify the extra work.

I agree with points made in other answers, but want to point out: if you're at Berkeley (I assume that's the UCB you mean) taking loads of grad classes and doing well, then you should get good letters and get into a top program without much trouble. Doing research isn't necessary for US PhD programs, and as discussed elsewhere on this site probably won't help all that much under normal circumstances anyway.

Also, if you haven't written papers before, you probably don't realize how time consuming it really is (at least to do a good job of it, and avoid mistakes---if it's poorly written, it might hurt your chances) and may take away from your other studies.

In summary, since you want to spend your time learning other things, I think you're better of doing that.