As this will -thanks to me being quite clueless- be a very open question I will start with the setup:

One nginx server on an old Raspi getting ports 80 and 443 routed from the access point and serving several pages as well as some reverse proxies for other sevices.

So a (very simplified) nginx server-block that looks like this:

# serve stuff internally (without a hostname) via http
server {
	listen 80 default_server;
	http2 on;
	server_name _; 
	location / {
		proxy_pass http://localhost:5555/;
                \# that's where all actual stuff is located
	}
}
# reroute http traffic with hostname to https
server {
	listen 80;
	http2 on;
	server_name server_a.bla;
	location / {
		return 301 https://$host$request_uri;
	}
}
server {
	listen 443 ssl default_server;
	http2 on;
	server_name server_a.bla;
   	ssl_certificate     A_fullchain.pem;
    	ssl_certificate_key A_privkey.pem;
	location / {
		proxy_pass http://localhost:5555/;
	}
}
#actual content here...
server {
	listen 5555;
	http2 on;
    	root /srv/http;
	location / {
        	index index.html;
   	} 
    	location = /page1 {
		return 301 page1.html;
	}
    	location = /page2 {
		return 301 page2.html;
	}
        #reverse proxy for an example webdav server 
	location /dav/ {
		proxy_pass        http://localhost:6666/;
	}
}

Which works well.

And intuitively it looked like putting Anubis into the chain should be simple. Just point the proxy_pass (and the required headers) in the "port 443"-section to Anubis and set it to pass along to localhost:5555 again.

Which really worked just as expected... but only for server_a.bla, server_a.bla/page1 or server_a.bla/page2.

server_a.bla/dav just hangs and hangs, to then time out, seemingly trying to open server_a.bla:6666/dav.

So long story short...

How does proxy_pass actually work that the first setup works, yet the second breaks? How does a call for localhost:6666 (already behind earlier proxy passes in both cases) somehow end up querying the hostname instead?

And what do I need to configure -or what information/header do I need to pass on- to keep the internal communication intact?