What semantic notions underlie "pull, drag" (in tractō) 🡒 "negotiate, bargain" (in 'treat')?
Etymonline below blazons the sense of "negotiate, bargain" in treat. Please see the green line for the sense of "pull, drag" from tractō.
I added the red lines beside 8(b) and 9, because these senses of tractō appertain to "negotiate, bargain". Negotiation and bargaining usually require discussion.
c. 1300, "negotiate, bargain, deal with," from Old French traitier "deal with, act toward; set forth (in speech or writing)" (12c.), from Latin tractare "manage, handle, deal with, conduct oneself toward," originally "drag about, tug, haul, pull violently," frequentative of trahere (past participle tractus) "to pull, draw" (see tract (n.1)).
Meaning "to entertain with food and drink without expense to the recipient by way of compliment or kindness (or bribery)" is recorded from c. 1500. Sense of "deal with, handle, or develop in speech or writing" (early 14c.) led to the use in medicine "to attempt to heal or cure, to manage in the application of remedies" (1781).
Oxford Latin Dictionary (2012 2 ed), pp 2154-5.