Homebrew installs more than you asked for, and keeps it all

Homebrew is two separate storage problems and the advice online only ever covers one of them. The cache of downloaded bottles is well known. The installed packages themselves are usually larger, and nothing suggests removing any of them.

See what is actually installed

du -sh /opt/homebrew 2>/dev/null
du -sh /opt/homebrew/Cellar/* 2>/dev/null | sort -h | tail -20

The Cellar is where the packages live, one folder per formula, and possibly more than one version inside each. The list is usually a surprise, because most of it is dependencies rather than things you asked for.

Dependencies nothing needs any more

When you remove a package, Homebrew leaves the dependencies it installed for it, because something else might need them. Often nothing does:

brew autoremove --dry-run
brew autoremove

The dry run lists exactly what would go. On a Mac that has had Homebrew for a few years this is regularly a dozen formulae, several of them large, and every one of them is something you never chose to install.

What you asked for, as opposed to what came along

brew leaves
brew list --formula | wc -l

brew leaves prints only the formulae that nothing else depends on, which is the list of things you actually installed. Compare its length with the total. The difference is the dependency tree, and it explains most of the Cellar.

Old versions, and the cache

brew cleanup --dry-run
brew cleanup -s

brew cleanup removes superseded versions and clears the download cache, and the -s flag makes it clear the cache more aggressively. That is the part covered in the Homebrew cache guide, which also explains why the space sometimes does not appear where you expect.

Casks are applications

Anything installed with brew install --cask is an ordinary Mac application in your Applications folder, and it counts there rather than in the Cellar. Removing one with brew uninstall --cask removes the app, and leaves the same support files behind that any uninstall leaves.