Intended behavior for Host header in Proxy scenario

[Jack Henschel]

Hello everyone,

during my last debugging session with Nginx I was wondering how and when
exactly Nginx passes upstream's hostname when proxying a request.

In particular, I have the following example:
> upstream backend {
>   server a.example.com:443;
>   server b.example.com:443;
> }

> server {
>   proxy_pass https://backend/path;
>   proxy_set_header Host $proxy_host; # default according to docs
> }

I observed that Nginx does not always pass the appropriate Host header
to the upstream server (i.e. "a.example.com" for "server
a.example.com:443" and "b.example.com" for "server b.example.com:443").

Is this observation correct or am I missing something?

Regards
Jack