I would first like to say, right off the bat, yes, the devs specifically put a tip in the main menu that says NOT to look for the secret, it will find you. However, I played through and beat every single level, clicking everywhere (as that was how you typically found secret endings for the previous I'm on Observation Duty games) and found nothing. Once I finally looked into it, though, I was disappointed to find that it was simply rng at the end of a full level.

Since there seems to be no other guides on how to unlock achievements (though I much appreciate the anomaly guides from the community), I had to scour through playthroughs to find this secret ending/achievement. This is how I came to find out it was simply rng after finishing a level, and was about to waste hours trying to unlock it. However, I continued to watch one playthrough in particular, https://www.youtube.com/watch?v=L6w-7YHMzBY (time stamp: 11:51) and to my delight the YouTuber starts to replay a level, but proceeds to quit out of it and gets the ending anyway! After trying it maybe 5-7 times, myself, simply starting and quitting a level immediately, I unlocked the secret ending!
You will know you've gotten the secret ending when the screen is all black, you hear some noise/music, and it doesn't load the main menu back up immediately. Instead, after a little bit it will give you a "yes or no" prompt. I believe I got the achievement just by getting the prompt at all, but I chose yes, as the YouTuber did in his video just to be safe.

While this may be cheesing it, I do not have the time or patience to sit through over 7 potential playthroughs of the same level over and over again to get one secret. I hope this helps you get your achievement and some new lore, and I also hope I don't disappoint the devs if they see this, as I really do enjoy their games! :)