The first one to send “shluchim” for kiruv purposes was the previous Rebbe
Not true. The Rashab sent shluchim to Georgia, who were largely responsible for reestablishing yiddishkeit there.
Before that I can’t think of any individuals who could be called “shluchim” in the current sense, whose entire purpose of moving somewhere was to bring yiddishkeit there, but as a previous commenter pointed out this is a matter of geography, not focus. When Jews were more geographically concentrated it was less necessary to relocate in order to reach them.
The Baal Shem Tov’s work was certainly “kiruv” in the current sense. He reached out to those who were neglected and in despair, whom the maggidim were telling that they were worthless and headed for gehenom and had no reason to serve Hashem, and he fought the magidim and started a whole movement to tell these people that Hashem valued them and they should serve Him and do mitzvos.
And yes, that absolutely did include those who were publicly eating treif or were intermarried or converted, but mostly it was people who were outwardly observant because there was no real alternative, but who were not observant in private, or not committed to observance.