Install wordpress in subdirectory with docker-compose and nginx

I am going to build a website with docker-compose.

When user enter the root directory, it goes to the web app. When the user enter the http://example.com/blog, it should redirect to the wordpress.

In order to do so, i have config the docker-compose like this

version: "3"

services:

  nginx:
    image: nginx:latest
    depends_on:
      - web-app
      - wordpress
    volumes:
      - ./nginx/nginx.conf:/etc/nginx/nginx.conf
    ports:
      - 80:80

  mysql:
    image: mysql:5.7.29
    container_name: mysql
    restart: always
    volumes:
      - ./data/mysql/data:/var/lib/mysql

  wordpress:
    depends_on:
      - mysql
    image: wordpress:latest
    ports:
      - 8000:80
    restart: always
    volumes:
     - ./data/blog:/var/www/html/wp-content
     - ./blog/wp-config.php:/var/www/html/wp-config.php

  web-app:
    build: ./app
    depends_on:
      - mysql
    restart: always
    command: npm start
    environment:
      - TZ=UTC
      - NODE_ENV=production

networks:
  default:
    external:
      name: common

And this is my nginx config

worker_processes auto;
events {
    worker_connections 1024;
}
http {
    include /etc/nginx/mime.types;
    default_type application/octet-stream;
    log_format main '[$time_local] $remote_addr - $request request_time: $request_time';
    access_log /var/log/nginx/access.log main;

    gzip on;
    gzip_http_version 1.1;
    gzip_vary on;
    gzip_comp_level 6;
    gzip_proxied any;
    gzip_types text/plain text/html text/css application/json application/javascript application/x$
    #                        make sure gzip does not lose large gzipped js or css files
    #                        see http://blog.leetsoft.com/2007/07/25/nginx-gzip-ssl.html
    gzip_buffers 16 8k;

    server {
        listen 80;
        charset utf-8;

        location /blog/ {
            proxy_set_header  Host               $host;
            proxy_set_header  X-Real-IP          $remote_addr;
            proxy_set_header  X-Forwarded-For    $proxy_add_x_forwarded_for;

            proxy_pass http://wordpress;
        }

        location / {
            proxy_http_version 1.1;
            proxy_set_header X-Real-IP $remote_addr;
            proxy_set_header Upgrade $http_upgrade;
            proxy_set_header Connection "upgrade";
            proxy_set_header Host $http_host;
            proxy_set_header X-NginX-Proxy true;
            proxy_redirect off;
            proxy_pass http://web-app:3000;
        }

    }
} 

And I have updated the wp-config.php and set the website url.

define('WP_SITE_URL', 'https://example.com/blog');
define('WP_SITEURL', 'https://example.com/blog');
define('WP_HOME', 'https://example.com/blog');

However, when I enter to https://example.com/blog, it return the ERR_TOO_MANY_REDIRECTS response.

I have searched a lot articles and some of that say it is because I am using cloudflare. How can I solve the above problem?