“Rav Schachter quotes a Chassam Sofer that there’s an Issur of Ba Tosif to make an extra hoiday. How, then could Chazal have made Channukah and Purim?”
We might answer with the following Svara: That Bal Tosif would be applicable if it were to undermine the *quality* of the yom. To clarify, if Purim were made into a full-fledged Yom Tov, melacha (other than food preparations) would be assur, Tefillin could not be put on, Levayas and a Pidyon HaBen would have to be postponed, etc…
Chazal were mesaken hanhagos (for Chanukah & Purim) that did not take away from the normal practices of the day.