The Battle at Boreth involved Kelpien, Ba'ul, Klingon, Section 31, and Starfleet forces, and was recorded from countless different angles by ship, shuttle, and drone sensors. It may very well be the most thoroughly documented event in Star Trek canon - better than the Battle of The Binary Stars. Apparently Starfleet took a vow to never speak of the incident, which explains why Spock never talks about his sister in TOS.
How many other witnesses know that Discovery was not destroyed?
It seems Starfleet just lost a top-secret prototype research vessel which can travel anywhere in the universe - and even to other universes - and all they do to find out what happened to it is ask 5 crew members, "Was it destroyed?" They do not seem at all concerned that Discovery could possibly have fallen into Klingon or Kaminari hands. Seriously, it was handled like someone just said their child lost a teddy bear in the mall. The evidence was overwhelming - from the massive tachyon burst the temporal rift caused, the complete lack of debris, and hundreds of sensor logs. But more important, the eye-witnesses! How many?
We have to ask if Starfleet even cares what happened to their secret vessel.