My understanding is that your research mentor knows you well. This might help your application, but it is hard to say not knowing how well tied in to Stanford they are currently and also given how selective Stanford is.
In an article in the alumni magazine a few years ago Stanford said that about 80% of applicants were academically qualified to attend and do well. You seem to be clearly in this 80%. Of course closer to 4% are accepted. These stats are somewhat stretched due to recruited athletes and legacy students (Stanford has quite a few athletic teams and does consider legacy status). However, having a research mentor who knows you and is associated with Stanford is a plus.
My wild guess is that your chances are similar to the overall acceptance rate, or maybe (?) marginally better.
Personally I loved Stanford and think that it is worth an application for a very strong student such as you. Of course it is a long way away for us east coast folks, but I think that it might be worth the travel. Whether it is worth the current cost of attendance is another issue (I got my master’s there a long time ago, so it was less expensive and the master’s was much quicker compared to a bachelor’s degree).
If you do go there, expect to work very hard, and be aware that since they are on the quarter system the end of the quarter comes up quickly and you better be ready.
Best wishes.