How to set up php processing for multiple locations in nginx?

Question

Nginx

Hello!
Set a password to access the Joomla admin panel in nginx:

location ^~ /administrator/ {
  auth_basic "Restricted";
  auth_basic_user_file /etc/nginx/.htpasswd;

The password request occurs correctly, i.e. when accessing ../administrator and ../administrator/index.php.
But the question is that for location ^~ /administrator/ you have to write the whole location ~* \.php$ again

location ~* \.php$ {
# размеры буффера
    fastcgi_buffer_size 128k;
  fastcgi_buffers 256 4k;
  fastcgi_busy_buffers_size 256k;
    fastcgi_temp_file_write_size 256k;
  try_files $uri = 404;
    fastcgi_split_path_info ^(.+\.php)(/.+)$;

# сокет php-fpm
    fastcgi_pass unix:/var/run/php/php7.4-fpm.sock;
    fastcgi_index index.php;
    fastcgi_param SCRIPT_FILENAME
  $document_root$fastcgi_script_name;
  include fastcgi_params;
  fastcgi_read_timeout 300;

Is this true or should it be optimized?