The list seems to be
- The bridge crew of USS Enterprise. We never see any non-bridge members interviewed, and given how badly damaged she was, it's likely they could claim they were occupied elsewhere if they did actually know.
- Ashe Tyler and L'Rell (plus however many Klingons saw it)
- Siranna (Saru's sister)
- Me Hani Ika Hali Ka Po
Presumably all the Section 31 ships were destroyed. The Klingons had no reason to divulge they were there, let alone that they helped the Federation. Siranna's situation is unknown, but it is probable that Saru let her know what he was about to do. Po is the ruler of her world, and diplomatic immunity applies. Ashe Tyler has no reason to tell them what happened either. It's likely that Pike brought him back to Earth as well.
We have to ask if Starfleet even cares what happened to their secret vessel.
Control was wholly a Starfleet invention. And that was a ton of ships they lost. If you dig too deeply into this, there's a chance others will dig deeply as well. It would not go well for the Federation to admit they accidentally created a homicidal AI that would have eventually succeeded in exterminating all sentient life in the quadrant. And you might not want to admit Control or Section 31 ever existed either.
Better to let Discovery go and accept the official cover story than to have others asking serious questions.
EDIT: Star Trek: Strange New Worlds expounds a bit on this in S1E1 Strange New Worlds
Pike asks what happened, as the Kileys were clearly not ready for first contact. Una glances at La'an for a moment, saying she was not cleared, but Pike dismisses that, asking how they got warp capabilility. Una replies that they had given it to them, during that final battle near Xahea, when Burnham opened the wormhole that sent her and the Discovery through to the future. They were less than one light-year out from the zero point of the wormhole, and between the Klingon ships and the Ba'ul fighters flown by the Kelpiens, there were more than a hundred warp signatures. Pike realizes the Kileys' telescopes would have been just powerful enough to detect all of it, and collected enough data to reverse-engineer a matter-antimatter reactor.
What's fascinating is how this plays out
Pike breaks the Prime Directive by deliberately revealing himself and the Enterprise to the Kileys. Robert April explains he was able to keep them out of trouble by "pulling strings" to find out what really happened. Because the Federation Council could not acknowledge the Discovery wormhole, they drop the whole incident.
In other words, the event is a bit better known than Discovery S2 let on.