PHP@7.1 is deprecated https://www.php.net/supported-versions.php.

So try to install with other repo

1 brew install openldap libiconv
2 brew tap exolnet/homebrew-deprecated
3 brew install php@7.1

https://devhoi.com/threads/install-brew-deprecated-php-version-php-7-1-5-6-7-0-on-brew-macos.25/