Here is my final solution.
On pihole (as root):
pihole-FTL --config webserver.paths.prefix /pihole
My location block:
location ^~ /pihole/ {
proxy_set_header Host $host;
proxy_set_header X-Real-IP $remote_addr;
proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
proxy_set_header X-Nginx-Proxy true;
rewrite ^/pihole/(.*)$ /$1 break;
proxy_pass http://localhost:8080/;
}