Princeton BSE degree vs BA degree? Need a princeton student or alumni to answer?

Hello! I am looking for a current student at Princeton or an alumni from Princeton because after doing some research I have gotten mixed answers.
I am wondering if, like Yale and Harvard, Princeton accepts students to the university as a whole, or is applying as BSE a separate admissions process to applying as a BA.
I know that you can easily switch majors from within the BSE school and you can easily switch majors from within the BA school. But if I apply as a BA on the application, can I switch to a BSE major, or vice versa, or is this not allowed? I am undecided on whether to apply Chemical engineering or Chemistry, and these are both different degrees. The Dean of Admissions states: “Majors are not considered binding. The only exception is for students who will be applying to a bachelors program in the arts or in science and engineering.”
Thoughts? Is Princeton like Yale and Harvard, where you can switch from anything to anything, or is Princeton like Columbia or Upenn, where you can’t switch in or out of engineering?

Also, is it possible to pursue a BA and BSE double major?

I doubt Princeton students are going to come here. You should probably just call the registrar’s office.

It would be best to keep the line of questions to one thread. Two threads with the same question produces confusion, not a broader set of responses.