c. 1200, "act of pulling or drawing; quantity of liquid that one drinks at a time," from Old English *dreaht, *dræht, related to dragan "to draw, drag" (see drag (v.)). The oldest recorded sense besides that of "pulling" is of "drinking" (perhaps "so much as is drawn down the throat at once"); compare drag (n.) in reference to an inhaling on a cigarette. It is attested from c. 1300 as "that which is drawn or written." In British English, it retains the functions that did not branch off with draft (q.v.).
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy).
<a href="https://www.etymonline.com/word/draughty">Etymology of draughty by etymonline</a>
Harper, D. (n.d.). Etymology of draughty. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/draughty