Q. Is it true that the Chasam Sofer says that not saying tachanun on Purim Kattan is a mitzva of the Torah?

A. Indeed Chasam Soffer (O.H. 208) does mention that the reading of the megilla, eating the seuda and shalach monos during Purim are only Rabbinical mitzvos.

However, even doing a small remembrance to the miracle of salvation on Purim and thanking Hashem for it, is a Biblical mitzva.
This includes not eulogizing a hesped or fasting, even on Purim Kattan as mentioned in Shulchan Aruch (O.H. 697: 1).

The mitzva, he explains, is the Kal Vachomer, mentioned in Megila (14a) “if from servitude to freedom we recite shira, so much more from death to life.”

Rabbi A. Bartfeld as revised by Horav Dovid Pam, Horav Aharon Miller, Horav Chanoch Ehrentreu Shlit’a and Horav Kalman Ochs Shlit’a.