"casual, occurring casually in connection with something else; of minor importance," 1640s, from Medieval Latin incidentalis, from incidens (see incident (n.)). The earlier adjective in this sense was incident (1520s). Incidentals (n.) "'occasional' expenses, etc.," is attested by 1707. Incidental music "background music," originally in operas, is from 1812.
common adverbial suffix, forming from adjectives adverbs signifying "in a manner denoted by" the adjective, Middle English, from Old English -lice, from Proto-Germanic *-liko- (cognates: Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko); see -ly (1). Cognate with lich, and identical with like (adj.).
Weekley notes as "curious" that Germanic uses a word essentially meaning "body" for the adverbial formation, while Romanic uses one meaning "mind" (as in French constamment from Latin constanti mente). The modern English form emerged in late Middle English, probably from influence of Old Norse -liga.
<a href="https://www.etymonline.com/word/incidentally">Etymology of incidentally by etymonline</a>
Harper, D. (n.d.). Etymology of incidentally. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/incidentally