update is indeed a deprecated alias for upgrade.
The aliases mentioned in the dnf manual are defined in the code. dnf alias is for user aliases.
Ideally, all packages include docs (so you can refer to them without Internet access), and all included docs are up to date. This is usually true for important or popular programs. Lesser used programs can sometimes fall behind. If you find any docs are outdated, incorrect, or missing, the best thing to do is fix it upstream, so that it benefits everyone using the software, not just Fedora.
man may be ancient, but it’s still the current system, at least for command-line programs. It’s not going away.
In the case of dnf, the manual on your system (man dnf) and the online docs have the same contents; the only difference is formatting. Some GNU programs like coreutils and bash provide extended docs in info format (compare info head vs man head).
Some packages include extra docs in /usr/share/doc. These might be a Fedora-specific README added by the package maintainer, or miscellaneous files from upstream that weren’t written for a proper system like man pages. Sometimes GUI programs dump HTML docs here and don’t link to it from a Help menu…
KDE Discover (and GNOME Software) not only handles rpm packages (like dnf), but also Flatpaks and firmware updates. See Software Repositories & Tools :: Fedora Docs