Piazza is asking me for a princeton.edu email address (I tried to sign up through the link you gave above).
Can I sign up for the course if I am not a Princeton student (or any student of a university, for that matter)?
https://piazza.com/product/features
To limit enrollment in your class, by default a school
email domain is required to self-enroll. If your school
does not provide students with school email addresses,
instead a class access code is automatically set to
limit enrollment in your class.