Checking for `HOMEBREW_NO_INSTALL_CLEANUP` was added in #18825, but this
breaks developers by switching them to the stable branch.
Setting `HOMEBREW_NO_UPDATE_CLEANUP` when `HOMEBREW_NO_INSTALL_CLEANUP`
is set seems like a relatively recent addition, so I don't think it
hurts to just remove it. We can add it back (correctly) if there are
users that need it.