That the descendants of Korah were not made extinct is clear from their authorship of several Psalms such as 42, 44, 45, 46, 47, 48, 49, etc.
Now let us return to the record in Numbers.
- Num 16:32 - simply says that the earth swallowed only those who were "with Korah" לְקֹ֔רַח. This does NOT say that Korah's descendants were killed and never mentions anything about his descendants. The closest we come is their immediate households בָּתֵּיהֶ֑ם which does not necessarily include all his family.
- Num 26:10 - same comment applies - no descendants of Korah are mentioned, only those who were with him, that is his followers or sympathizers.
Thus, we find no suggestion that Korah's entire family and all his descendants were killed in the rebellion of Num 16. This is confirmed by Num 26:11 and the numerous psalms written by Korah's descendants.
The Cambridge commentary correctly observes in it remarks in Num 26:11 -
- "and the sons of Korah died not" There is no mention of Korah’s family in ch. 16, but the inference might naturally be drawn from
Numbers 26:32 that they were included in his body of adherents. This
inference the writer felt it necessary to check, because in his day
‘sons of Korah’ were found in Jerusalem. They were a subdivision of
the Levites, a guild which formed one of the temple choirs. To their
hymnbook belonged Psalms 42, 44-49, 84 f., 87 f. In Numbers 26:58
(below) they are called ‘the family of the Korahites.