From Terminal
# install dependencies
brew install autoconf # required by pecl
brew install libzip
# install zip extenion in your selected MAMP PHP version
ls /Applications/MAMP/bin/php/
cd /Applications/MAMP/bin/php/php[Version]bin
pecl install zip
# edit php.ini in your selected MAMP PHP version
ls /Applications/MAMP/conf/p*
cd /Applications/MAMP/conf/php7.3.8/
echo "extension=zip" >> php.ini
It seemed like it wasn't running the right composer or php or something. After installing the zip.so I still had to run it by explicitly specifying paths for my php, ini and composer...
/Applications/MAMP/bin/php/php7.4.9/bin/php -c "/Library/Application Support/appsolute/MAMP PRO/conf/php7.4.9.ini" /Applications/MAMP/bin/php/composer update