nginx 4xx when proxying pubblic websites

Goal: I wish to build a simple reverse proxy with nginx that can takes any public domain as an input and outputs the same website just fully proxied, similar to this website.

Problem: Most websites will return a forbidden or some other 4xx or 5xx error. I currently suspect it has something to do with the headers, specially the host header. I noticed that removing it, causes a 301 to the original website.

The road so far, aka my full conf

site.conf

    server {
    listen                  443 ssl http2;
    listen                  [::]:443 ssl http2;
    server_name             mydomain.com;
    root                    /var/www/mydomain.com/public;

    # SSL
    ssl_certificate         /etc/letsencrypt/live/mydomain.com/fullchain.pem;
    ssl_certificate_key     /etc/letsencrypt/live/mydomain.com/privkey.pem;
    ssl_trusted_certificate /etc/letsencrypt/live/mydomain.com/chain.pem;

    # security
    include                 nginxconfig.io/security.conf;

    # index.php
    index                   index.php;

    # reverse proxy
    location / {
        proxy_pass https://somedomain.com:443;
        include    nginxconfig.io/proxy.conf;
    }

    # additional config
    include nginxconfig.io/general.conf;
}

security.conf

# security headers
add_header X-XSS-Protection          "1; mode=block" always;
add_header X-Content-Type-Options    "nosniff" always;
add_header Referrer-Policy           "no-referrer-when-downgrade" always;
add_header Content-Security-Policy   "default-src 'self' http: https: data: blob: 'unsafe-inline'; frame-ancestors 'self';" always;
add_header Permissions-Policy        "interest-cohort=()" always;
add_header Strict-Transport-Security "max-age=31536000; includeSubDomains" always;

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

proxy.conf

proxy_http_version                 1.1;
proxy_cache_bypass                 $http_upgrade;
proxy_ssl_server_name              on;

# Proxy headers
proxy_set_header Upgrade           $http_upgrade;
proxy_set_header Connection        $connection_upgrade;
proxy_set_header Host              $host;
proxy_set_header X-Real-IP         $remote_addr;
proxy_set_header Forwarded         $proxy_add_forwarded;
proxy_set_header X-Forwarded-For   $proxy_add_x_forwarded_for;
proxy_set_header X-Forwarded-Proto $scheme;
proxy_set_header X-Forwarded-Host  $host;
proxy_set_header X-Forwarded-Port  $server_port;

# Proxy timeouts
proxy_connect_timeout              60s;
proxy_send_timeout                 60s;
proxy_read_timeout                 60s;

and finally nginx.conf

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

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

# assets, media
location ~* \.(?:css(\.map)?|js(\.map)?|jpe?g|png|gif|ico|cur|heic|webp|tiff?|mp3|m4a|aac|ogg|midi?|wav|mp4|mov|webm|mpe?g|avi|ogv|flv|wmv)$ {
    expires    7d;
    access_log off;
}

# svg, fonts
location ~* \.(?:svgz?|ttf|ttc|otf|eot|woff2?)$ {
    add_header Access-Control-Allow-Origin "*";
    expires    7d;
    access_log off;
}

# gzip
gzip            on;
gzip_vary       on;
gzip_proxied    any;
gzip_comp_level 6;
gzip_types      text/plain text/css text/xml application/json application/javascript application/rss+xml application/atom+xml image/svg+xml;

As you can see the configuration is generated by nginxconfig.io and seems pretty legit. Any ideas about what may be wrong?