A more formal definition of Baal Nefesh…
Rashi in Chullin 6a defines a Baal Nefesh as “a kosher person.”
In Pesachim 40a (where the Gemara says in a particular case of chametz, that for a baal nefesh it is assur) there are two versions of Rashi defining a Baal Nefesh. One is as a “chasid” and the other is as a “Yirei Shmayim hachared al nafsho.”
Rabbeinu Chananel defines a Baal Nefesh as “A person who distances himself from sin and is very careful with himself.”
(In Shulchan Aruch Yorah Deah the Ramah in 116:7 says “baal nefesh yachmir” and the Mishne Brura also uses the term “Ba’al Nefesh Yachmir” on occasion, some other instances of Baal Nefesh being referred to in psak.)