As has been pointed out before, the depiction in Discovery of Section 31 as an open, legal organization within Starfleet Intelligence, complete with badges, is at odds with a rogue group unaccountable to anyone in the 24th century. The question is how Section 31 leaves legitimacy and goes rogue and into hiding. I feel the answer might have been provided in "Light and Shadows". If you haven't seen it, stop reading as spoilers are ahead: Spoiler Sarek sends a confused and incoherent Spock to Section 31, over Amanda's objections, believing that they will safely extract the Red Angel info out of Spock's mind and cure him. He does this in good faith and he does not seem to realize that Section 31 has nefarious intentions regarding Spock. However, once Spock is in Section 31 hands, assuming Mirror Georgiou is telling Burnham the truth, then there is no attempt to safely extract info out of Spock's mind. Not even with a mind meld. S31 was going to use a machine to brutally extract Spock's memories and leave his mind permanently damaged. Only Mirror Georgiou's warning to Burnham caused Burnham to break Spock out and get him to safety. At some point, Sarek is going to hear about what Section 31 did. And it's safe to assume that, even with his Vulcan emotional control, he will not be happy to put it mildly. When Spock recovers, while he may understand that Sarek did not know S31 was going to harm him, he may still be disappointed at Sarek's failure of logical deduction to realize S31 was villanous and this may contribute to their lack of communication until TOS, to provide continuity with "Journey to Babel". Being that Sarek is a powerful Federation figure, could he be the one who purges Section 31 from Starfleet Intelligence and sends them into hiding?