1590s, "the functions of a general" (a sense now obsolete); 1620s, "the office of a general;" from general (n.) + -ship. The meaning "management of an army; the military skill or conduct of a commander" is by 1770.
late 14c., "whole class of things or persons, a broad classification, a general truth," from general (adj.). Meaning "commander of an army" is 1570s, shortening of captain general, from French capitaine général. The English adjective was affixed to civic officer designations by late 14c. to indicate superior rank and extended jurisdiction.
word-forming element meaning "quality, condition; act, power, skill; office, position; relation between," Middle English -schipe, from Old English -sciepe, Anglian -scip "state, condition of being," from Proto-Germanic *-skepi- (cognates: Old Norse -skapr, Danish -skab, Old Frisian -skip, Dutch -schap, German -schaft), from *skap- "to create, ordain, appoint," from PIE root *(s)kep-, forming words meaning "to cut, scrape, hack" (see shape (v.)). It often forms abstracts to go with corresponding concretes (friend/friendship, etc.).
<a href="https://www.etymonline.com/word/generalship">Etymology of generalship by etymonline</a>
Harper, D. (n.d.). Etymology of generalship. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/generalship