How to block API calls outside its own domain ( NGINX )

Question

I have a website running with NGINX where I have an API and a Vue APP, let's say API it's on api.example.com and the Vue APP it's on www.example.com and I have some requests that I can't use a middleware or something, so I would like to know how can I prevent the API from being called outside example.com.

I'm testing it right now with my Vue APP running on localhost:8080, and I still can access it.

My current NGINX config for the API is

server {

  server_name api.example.com;
  root /var/www/api/public;

  add_header X-Frame-Options "SAMEORIGIN";
  add_header X-Content-Type-Options "nosniff";

  index index.php;

  charset utf-8;

  location / {
      try_files $uri $uri/ /index.php?$query_string;
  }

  location = /favicon.ico { access_log off; log_not_found off; }
  location = /robots.txt  { access_log off; log_not_found off; }

  error_page 404 /index.php;

  location ~ \.php$ {
      fastcgi_pass unix:/var/run/php/php8.1-fpm.sock;
      fastcgi_param SCRIPT_FILENAME $realpath_root$fastcgi_script_name;
      include fastcgi_params;
  }

  location ~ /\.(?!well-known).* {
      deny all;
  }

  listen [::]:443 ssl ipv6only=on; # managed by Certbot
  listen 443 ssl; # managed by Certbot
  ssl_certificate /etc/letsencrypt/live/api.example.com/fullchain.pem; # managed by Certbot
  ssl_certificate_key /etc/letsencrypt/live/api.example.com/privkey.pem; # managed by Certbot
  include /etc/letsencrypt/options-ssl-nginx.conf; # managed by Certbot
  ssl_dhparam /etc/letsencrypt/ssl-dhparams.pem; # managed by Certbot
}

I tryed to use

add_header Access-Control-Allow-Origin "https://www.example.com";

But I got this

Access to XMLHttpRequest at 'https://api.example.com/api/what' from origin 'https://www.example.com' has been blocked by CORS policy: The 'Access-Control-Allow-Origin' header contains multiple values '*, https://www.example.com', but only one is allowed.