I'm speculating. That's why I said "seems to be".
If Section 31 has a use for you, they'll make you aware of them, as Sloan did to Bashir in "Inquisition". Bashir was a Lieutenant. Worf was a Lt. Commander, and if Section 31 didn't need him, they wouldn't approach him and they wouldn't approach him. Therefore Bashir, who is of lower rank, would know about Section 31 and Worf wouldn't.
Bashir went to Sisko and Sisko went to Starfleet Command. They confirmed and denied nothing. Chances are Sisko inquired and passed along until hit a wall with someone who knew but only told Sisko they'd look into it. A similar thing happened to Bashir when he was trying to find a cure for the disease Odo had in "Tacking Into the Wind". The episode reveals Odo was infected with the disease by Section 31 in the "Homefront"/"Paradise Lost" two-parter and that he unknowingly spread the disease to the rest of the Founders in "Broken Link". Sisko, off-screen shortly before the end of "Inquisition" probably ran into the same wall Bashir did during "Tacking Into the Wind".
When Bashir told Sloan he'd report Section 31, Sloan said he wouldn't lose any sleep over it. If Bashir's report was part of a log that was available to Starfleet Officers with his level of Secuirty Clearance and Sloan still wouldn't lose any sleep over it, then it wasn't much concern to him if it was known by Starfleet Officers who bothered to look it up. If it was part of Sisko's log, and restricted to those with Sisko's Security Clearance and above, Sloan would be even less concerned. Section 31 would be known to anyone who would've bothered to look them up in Sisko or Bashir's logs, but if you didn't bother to look it up, you still wouldn't know even if they
were in the logs. And if Sisko and Bashir didn't discuss Section 31 in their logs, then that makes what they know even less accessible.
Either way, Section 31 was part of Starfleet right from the beginning as per Sloan's claim at the end of "Inquisition", which is backed up in ENT Season 4. And Section 31, because it was part of the Charter, had to have been known by those in the Admiralty would would have familiar with the Charter. Which brings me to another point: why would any Starfleet Officers
not be aware of the Charter, unless it was extreme fine print, which is possibly something Section 31 operatives are counting on. Who reads fine print? The best way to hide sometimes is right in plain sight.
Getting back to "Homefront", "Paradise Lost", and "Extreme Measures" though, the Dominion seem to be the greatest threat to the Federation in the 24th Century besides the Borg. At least that's the case that was made in "Homefront". Section 31, of course, would want to deal with this threat. And Starfleet was dealing with this threat. If Starfleet and Section 31 want to defeat the same enemy, the Dominion, and Admiral Ross has been heavily involved with the war effort, then it makes sense that Sloan and Admiral Ross would collaborate. Sisko and Garak already did the dirty work of bringing the Romulans into the war effort on the Federation's side. Section 31 took the next step in making sure an influential Senator was elevated to a position within the Romulan Senate to make sure the Romulans would stay on the Federation's even after the War ends. Starfleet can't always turn to Garak, so it makes sense that they would turn to Section 31 and, if Starfleet has done such things in the past, then it also explains why Starfleet Command approved of Sisko and Garak's plan in "In the Pale Moonlight" in the first place.
But now it's a Monday morning... and I have to get ready to do other things.