How to update Ruby with Homebrew?

brew upgrade ruby

Should pull latest version of the package and install it.

brew update updates brew itself, not packages (formulas they call it)

I would use ruby-build with rbenv. The following lines install Ruby 3.1.2 and set it as your default Ruby version:

$ brew update
$ brew install ruby-build
$ brew install rbenv

$ rbenv install 3.1.2
$ rbenv global 3.1.2