I'd bet money we're not going to see or hear about Section 31 at all in Picard. Primarily because they were just on Discovery, they're getting their own series, and it's too easy to use them as a scapegoat in this series. I also think this show wants to look squarely at the shortcomings of Starfleet itself, by people who are now outside of it. And besides everything else, the Zhat Vash already fill the role S31 would've here. So Section 31 in Picard would be redundant.
Discovery's portrayal of Section 31 was awful, I don't want Picard to have anything to do with S31 other than perhaps a name. DS9 was the first and last time we should have heard of them, not everything is down to S31, nor are they all seeing and all powerful as people seem to think.
I always thought the main point of Section 31 was that hardly anyone knew about them in the first place. Now, almost every show wants to show them in plain view. So ITD and Discovery had them too.
It's really overdone. The first few times in DS9 were interesting, but constantly showing them is like what happened with the Borg on Voyager.