GROK gives the etymological root meaning of storge (family love):

 

Fulltext version:

The Greek word storge refers to familial love, particularly the natural affection between parents and children or within a family. Its etymological root lies in the Proto-Indo-European (PIE) root ster- or stor-, which conveys the sense of “care,” “affection,” or “nurturing.” This root is associated with instinctive, protective, and enduring bonds, often tied to familial or communal care.

In Greek, storge derives from a verbal root related to stérgein, meaning “to love” or “to feel affection,” especially in a familial context. The term emphasizes a deep, instinctual, and often unconditional love, distinct from other Greek words for love like agape (selfless love), philia (friendship), or eros (sexual desire). The etymology reflects a foundational concept of natural attachment and care inherent in extended family relationships.