1620s, "kindred, partaking of the same nature or natural characteristics," from assimilated form of Latin com "with, together" (see con-) + genialis "of birth," thus, "kindred" (from PIE root *gene- "give birth, beget," with derivatives referring to procreation and familial and tribal groups). Sense of "agreeable" is first recorded 1711 on the notion of "having natural affinity." Also compare congenital.
word-forming element making abstract nouns from adjectives and meaning "condition or quality of being ______," from Middle English -ite, from Old French -ete (Modern French -ité) and directly from Latin -itatem (nominative -itas), suffix denoting state or condition, composed of -i- (from the stem or else a connective) + the common abstract suffix -tas (see -ty (2)).
Roughly, the word in -ity usually means the quality of being what the adjective describes, or concretely an instance of the quality, or collectively all the instances; & the word in -ism means the disposition, or collectively all those who feel it. [Fowler]
<a href="https://www.etymonline.com/word/congeniality">Etymology of congeniality by etymonline</a>
Harper, D. (n.d.). Etymology of congeniality. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/congeniality