secured WordPress login with nginx htpasswd prevents from woocommerce logout

i've protected my /wp-admin/ and wp-login.php with htpasswd in nginx.

this is the .conf file

server {
    listen [::]:443 ssl http2;
    listen 443 ssl http2;
    server_name www.url;

    access_log   /var/log/nginx/url.access.log;
    error_log    /var/log/nginx/url.error.log;

        client_max_body_size 16M;
        large_client_header_buffers 4 32k;
        # live system
        root /var/www/prod-domain;
        index index.php;
        # in case of maintenance use this directory
        # root /var/www/maintenance;
        # index index.html;

        location / {
                try_files $uri $uri/ /index.php?$args;
        }
        # protect admin area
        location /wp-admin/ {
               auth_basic "Backend Login";
               auth_basic_user_file /var/www/.htpasswd;
        }
        # allow file from admin area for frontend login/registration
        location /wp-admin/js/password-strength-meter.min.js {
               satisfy any;
               allow all;
        }
        # also protect wp-login file
        location = /wp-login.php {
               auth_basic "Backend Login";
               include snippets/fastcgi-php.conf;
               auth_basic_user_file /var/www/.htpasswd;
               fastcgi_pass unix:/run/php/php7.4-fpm.sock;
        }
        location ~ \.php$ {
      fastcgi_pass unix:/run/php/php7.4-fpm.sock;
      include         fastcgi_params;
      fastcgi_param   SCRIPT_FILENAME    $document_root$fastcgi_script_name;
      fastcgi_param   SCRIPT_NAME        $fastcgi_script_name;

      fastcgi_buffers 16 16k;
      fastcgi_buffer_size 32k;
    }

Problem: if you want to logout in woocommerce as customer, you can't. the logout process also use the wp-login.php and the browser prompt the login screen for htpasswd

can i exclude the process to allow the logout?

it looks like: wp-login.php?action=logout&redirect_to=https%3A%2F%2Fwww.url%2Fmein-konto%2F&_wpnonce=78d2a420af