How to configure nginx better to reduce redundant system calls when APIs are called?

It looks like you are dealing with try_files performance issue. You can get rid of unnecessary stat system calls by eliminating try_files from your configuration.

The try_files directive provides a nice and simple boilerplate for creating SEO-friendly website.

However, the downside of this simplicity comes with an added cost of unnecessary stat system calls.

Since you know that, for e.g. all /api/ URLs must be routed through your PHP, there is no need to check any files for existence there and you can route through your Laravel bootstrap file unconditionally, e.g.:

location /api/ {
    fastcgi_param SCRIPT_FILENAME $document_root/index.php;
    include fastcgi_params;
    fastcgi_pass unix:/var/run/php-fpm/example.com.sock;
}

Moreover, in general, you want to have NGINX cache information about file/directories existence. This can be achieved through open_file_cache.