Surprising you haven't come across a man page that basically says "We couldn't be bothered putting everything in here, check out the info page on it instead."
I feel like I find myself on one of those every 6 months or so.
That's funny, I had the opposite experience. When I found out that info was the GNU projects recommended way of documentation, I was all on board. Then I tried using it, and it couldn't find most CLI software I used. So I downloaded the texinfo archives... and that still lacked probably 50% of the commands I tried to look up.
Then I searched up how to get info pages for this or that tool, and someone on StackOverflow had said that it was woefully incomplete and outdated at this point.
The "info" thing was a misguided attempt by a crazed bunch of emacs zealots to usurp the rightful position of "man". Probably GNU's worst idea. It persisted in having some popularity for a decade or more but is now mostly forgotten I think. Despite having used Debian for the past ten years straight I've only just now found out that info doesn't even get installed by default any more.
Eh, to be honest, manpages aren't particularly good as either documentation or quick references (hence the popularity of tldr), and info is intended primarily for the sort of long-form, comprehensive documentation that would be awkward to fit in a manpage. Also, texinfo documents can easily be exported to HTML, so one format can be used for both online and offline docs. It's an admirable effort, if nothing else.
I'd have liked it a lot better if it had been intended and used as a place to put the more extensive documentation that isn't really appropriate for a man page, while leaving the man pages as they were. Instead, I learned about it back in the day by being frequently annoyed at missing man pages for basic tools, which had been replaced with suggestions to look at 'info' instead, which always seemed to be much less concise and have a worse UI.
Can you provide any source that it was created or initiated by what you call 'a crazed bunch of emacs zealots', or that the goal was to 'unsurp the rightful position of "man"'. Quite bold statements that are unlikely to be true imho.
man is standard Unix manual pages, while info is a documentation format introduced/popularised by GNU. info pages usually have a lot more information (sometimes including tutorials, guided examples, links to different pages and sections, etc (depending on the project maintainer obviously)) but man pages are the standard and basically everything has one. If you run info [program] for something without a dedicated info page, it will show the man page instead.
My impression tldr/cheat: Explains most popular arguments using as little words as possible man: Explains the entire command using a more technical tone info: Explains the entire command in slightly more informal tone. Can feel wordier as a result, but on the flipside it connects alternative/related commands in a logical way
I since switched to tldr (for the offline/caching functionality, I think?), but for the longest time I just used a wrapper function that did exactly this in my shell configuration. Something a bit like this: