Relative path link ignores proxy nginx

Question

Gitlab server running pages at https://pages.example.com
Gitlab pages correctly setup to serve one page at https://example.com/ instead of https://user.pages.example.com
Because inabilty to cname from https://user.pages.example.com/ to https://example.com with google domains, I have an nginx reverse proxy setup as such:

server {
    server_name example.com;

    location / {
        proxy_pass https://user.pages.example.com;
    }

    listen 443 ssl;
    ssl_certificate /etc/letsencrypt/live/example.com/fullchain.pem; # managed by Certbot
    ssl_certificate_key /etc/letsencrypt/live/example.com/privkey.pem; # managed by Certbot
}

Works fine when going to https://example.com (shows https://example.com rather than https://user.pages.example.com)
Link from index.html on that page goes to ./folder/ then url switches to https://user.pages.example.com/folder/ (bad)
Should go to https://example.com/folder/

I am stumped as to how to fix.