FWIW, authors Hancock and Boylan in The Oswald Puzzle do a very thorough analysis of all this and conclude that (1) Oswald was not a false defector or a witting participant in any intelligence activities but (2) may well have been an unwitting tool in one of Angleton's mole hunts. In other words, he wasn't "sent" at all, but his "going" may have served a mole-hunt purpose of which he was completely unaware.
We know that Angleton was duped by the British traitor Kim Philby, yes?
Well, Newman says father-figure-requiring Angleton was also duped by his mole-hunting superior, Bruce Solie, and that Solie very probably visited Philby -- to learn from The Master how best to manipulate Angleton -- in Beirut in February 1957, as indicated by some old travel documents which were published on geneology.com in 2010 and found by Newman around 2017.
Factoids: We know that Solie "cleared" KGB false defector Yuri Nosenko in October of 1968, that he helped another probable mole by the name of Leonard V. McCoy "lose" former defector Nicholas Shadrin to KGB kidnappers in Vienna in 1975, and that, according to British researcher and National Archives habitue Malcolm Blunt, he was "all over the Kennedy investigation and all over Clay Shaw for Jim Garrison" Read Tennent H. Bagley's
Spy Wars for the details for the first two and watch Blunt's 10 September YouTube interview on Yuri Nosenko for the latter.
Oh yeah, and that Solie hid Office of Security documents on Oswald from the Church Committee and the HSCA.
Heck, even Joan Mellen writes about that, but blames it on Angleton of course.
Rhetorical question: Can you not countenance the possibility that Angleton's confidant, mentor, and mole-hunting superior, Bruce Solie in the mole-hunting Office of Security, was a KGB mole, and that he sent (or duped Angleton into sending) Oswald to Moscow in 1959 as an OSTENSIBLE "dangle" in what Angleton thought was a "normal" CIA mole hunt -- for "Popov's U-2 Mole" / "Popov's Mole" -- but which was really a planned-to-fail "mole hunt" controlled by the KGB with the two-fold goal of 1) protecting the mole (Bruce Solie), and 2) tearing the Soviet Russia Division apart?