My favorite Bullshit Job was my very own. There was an employee that was hired only because, well I couldn't say No during the interview.
He had nothing to do so they turned him into a human website health checker. He had a page with dozens of iframes of all our websites. He would spend the day refreshing the page, reloading the iframes in intervals. If any failed to load he would report them.
Not knowing what the page was for, i was asked to automate refreshing each iframe after an interval. This meant, he wouldn't have to click the reload button anymore. Just sit and wait until a website failed. I thought his job was bullshit. Until, I realized that I had just automated a bullshit job.
This reminds me of a job that I had almost a decade ago. Arguably, it's less bullshit than the one you describe, but I think it's close. At the time, it wasn't that uncommon of a job in the animation industry.
The company was a medium-sized animation studio that at the time was doing cut-scenes for a AAA game. My job was to literally stare at a screen with a list of jobs and available computers in the "render farm" and, if any of them turned red or stopped responding, to walk downstairs and press the reset button on the corresponding box. I'd say 80% of my days were just staring at that screen. It felt like the stupidest job ever, even though there was some utility to it, but I was too inexperienced at coding at the time to automate my job.
To kill the boredom, I learned some Python and wrote a Hangman game. That's when I realized I was better off becoming a software engineer and started the career that I have now.
He had nothing to do so they turned him into a human website health checker. He had a page with dozens of iframes of all our websites. He would spend the day refreshing the page, reloading the iframes in intervals. If any failed to load he would report them.
Not knowing what the page was for, i was asked to automate refreshing each iframe after an interval. This meant, he wouldn't have to click the reload button anymore. Just sit and wait until a website failed. I thought his job was bullshit. Until, I realized that I had just automated a bullshit job.
Longer version: https://idiallo.com/blog/the-40-million-dollar-job