Didn't disclose ethnicity on Common App... Should I contact admissions to tell them mine?

Back to my 1st point – the anti-Asian bias is very debatable here on CC and elsewhere. I see no discrimination vs. Asian Americans at schools like Princeton per se. I see lots of discrimination against “boring” applicants at schools like Princeton. Thus, your goal is not to be in the “boring” pile – not the “Asian American” pile. That’s my take on things at least.