1570s, of a house, town, etc., "to be in a certain position" (implied in seated), from seat (n.). Of diseases, in the body, from 1610s (hence deep-seated). Transitive sense of "locate, settle, place permanently" is from 1580s.
The meaning "cause to sit, place on a seat" is from 1590s, especially "cause to sit on a throne or other seat of dignity." From c. 1600 as "set or secure in its proper place," hence many extended senses in mechanics. Of a theater, etc., "afford seating accommodations for," by 1830.
<a href="https://www.etymonline.com/word/deep-seated">Etymology of deep-seated by etymonline</a>
Harper, D. (n.d.). Etymology of deep-seated. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/deep-seated