Regarding the press conference: He supposedly had a drink with the President not long ago

They aren't exactly a reliable news outlet, but the article is so specific
(though I wonder if there are any reliable news outlets these days)
so this might be self-generated propaganda from Song Young-gil's side.
https://www.ilyoseoul.co.kr/news/articleView.html?idxno=522748
It says that during a press conference, it was mentioned that he opened some Chinese liquor at the Blue House not long ago and stayed out quite late.
It also says Song Young-gil advised not to dwell on reappointment or the dismissal of public prosecution.
And it claims the core group of four politicians assisting President Lee Jae-myung with political affairs are
Kang Hoon-sik, Kim Min-seok, Song Young-gil, and Jung Sung-ho...
Kim Min-seok decides "what" to do, Kang Hoon-sik decides "how" to do it,
Jung Sung-ho decides "with whom" to do it, and Song Young-gil decides "what not to do."