The thing about post-DS9 shows making Section 31 show up all the time is that you didn't have to do that at all. Starfleet already has Starfleet Intelligence, and they do espionage/retrievals/general Spying all the time without the need to involve 31. I mean, how many times does someone go on a secret mission in TNG (before they invented Section 31) just with normal Starfleet Intelligence?
And then they invent them for DS9 and suddenly in Discovery Section 31 is hunting down a garden variety mentally ill murderer (Spock with a beard, no, not this one. Other Spock with a beard.) Like, why are they doing that? This is only regular classified. And it's relatively straightforward case! You don't need to pull out the war criminal force for this. They're not breaking any laws nor do they need to cover up anything from other governments.
It makes sense Georgiou is in Section 31, because drafting her is too unethical for normal Starfleet. You could argue same with Ash Tyler, plus they have to cover up their involvement in Klingon politics with him. But using her and others to hunt down Spock makes no sense. He's at his mother's house, guys. We don't space CIA on this case.
But you know, the allure of these little tight leather outfits. And sexy shiny black badges, ooh. Let's have Section 31 take the dog out for a walk next or something, it's not like they're busy.
*and yes i know that the red angel thing will probably be important and that's why they're on this. but he can still be retrieved by normal starfleet, bc they have unquestionable grounds to do so. using the secret force for it only points this out as unusual, when they already have a perfect cover that doesn't need any additional lies, him killing people.