I'm willing to bet your second option, "they erased all records of it..." is the most likely answer.
Upon their return to the origin universe, I could see the Discovery making the report to Starfleet, who would then catalogue and classify the information as Top Secret. Or it's possible that they didn't even classify it; it just helped confirm scientific speculation that parallel universes exist. However, since the ability to get there involved some kind of malfunction with the spore drive (and we must assume this leads to the spore drive being classified as far too dangerous to use), no one ever gave travel between parallel universes a second thought.
So this became nothing more than a scientific curiosity, one that Kirk knew nothing about. (Let's face it... in Star Trek's future, the amount of scientific knowledge available would be incredible! There's no way Kirk could know about every type of anomaly, parallel universe, scientific theory, etc.). And, the ONE person who might know about this report, Spock, was left back in the original universe, so he wasn't there to tell Kirk about this one paper he read at some point that proved the existence of a parallel universe where everyone existed in a slightly different form.
It's also possible that they'll just use some kind of "Enterprise" style big reset button and everyone's memories will be wiped in the process of returning to our universe.
However, given how vast the amount of knowledge must be by the time of Star Trek, it wouldn't surprise me if Kirk knew nothing about it... some of our best scientists today may know TONS of stuff about a subject, but little about something else. There are limits to what we can be exposed to, after all!
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