Homebrew formula/package php is compiled with the zip extension enabled by default.
Homebrew is Homebrew, it's not MacPorts or any other Linux package manager. There's no need to install another package to enable the zip extension. Please check the fact before report the problem.
# https://github.com/Homebrew/homebrew-core/blob/48a3a49c57b22eb1450b01e7867cf054a89c5a7b/Formula/php.rb#L31
class Php < Formula
desc "General-purpose scripting language"
homepage "https://www.php.net/"
url "https://www.php.net/distributions/php-7.3.10.tar.xz"
sha256 "42f00a15419e05771734b7159c8d39d639b8a5a6770413adfa2615f6f923d906"
...
depends_on "libsodium"
depends_on "libzip"
depends_on "openldap"
...
--enable-wddx
--enable-zip
--with-apxs2=#{Formula["httpd"].opt_bin}/apxs
...
--with-libedit#{headers_path}
--with-libzip
--with-mhash#{headers_path}
...
