This works! However it only works fully if WordPress permalinks are set to simple?p=123. For example permalinks set to %postname% would produce links like /blog/hello-world which produce a 404 error.

interestingly navigating to the admin panel blog/wp-admin/ works fine.

Here is my current Nginx config after I added your comments. How would I change it to enable post-name permalinks to work?

server {
    listen 80 default_server;
    listen [::]:80 default_server;

    root /var/www/html;

    index index.php index.html index.htm index.nginx-debian.html;

    server_name 138.197.31.86;

    #location = /favicon.ico { log_not_found off; access_log off; }
    #location = /robots.txt { log_not_found off; access_log off; allow all; }
    #location ~* \.(css|gif|ico|jpeg|jpg|js|png)$ {
    #    expires max;
    #    log_not_found off;
    #}

    location / {
        proxy_pass http://localhost:8081;
        proxy_http_version 1.1;
        proxy_set_header Upgrade $http_upgrade;
        proxy_set_header Connection 'upgrade';
        proxy_set_header Host $host;
        proxy_cache_bypass $http_upgrade;
    }

    location /blog {
        try_files $uri $uri/ /index.php$is_args$args;
    }

    location ~ \.php$ {
        include snippets/fastcgi-php.conf;
        fastcgi_pass unix:/run/php/php7.0-fpm.sock;
    }

    location ~ /\.ht {
        deny all;
    }
}