Someone who ate a cazayis of pas and other foods that brought him to “c’dei saviah” is his chiyuv in Bircas HaMazon d’oraisa or d’rabbanan.
Because he has become satiated from a bread meal, where the entire meal is considered “secondary” to the bread, his obligation will be a Torah obligation.
This is apparent from the ruling of the Magen Avraham concerning somebody who eats only a kezayis of mezonos, but must wash and bentch because of other foods he eats that bring him to satiation.
Clearly, the problem the Magen Avraham is concerned with is the person’s satiation, and although it is provided by other foods, because it is part of a bread (or pas ha-ba be-kisnin) meal he is obligated (on a Torah level) to bentch.
There is some room to debate this matter when foods that are totally unrelated to the bread are eaten as part of the meal. The assumption for the halachah above is that all foods, such as meat and fish, are secondary to the bread.