Nothing strange. I check sources with dotpeek, X-Forwarded* headers does not using on login request. I add proxy_set_header Host $http_host; to nginx config for fix.

Nothing changed. I try with null value in base url and "https://nuget.medinfocenter.ru/" value

Cookie after authtification does not save because domain does not same, my proget instance url nuget.medinfocenter.ru but in cookie I see domain localhost

My nginx config

    location / {
            proxy_pass http://localhost:8000;

            proxy_set_header X-Forwarded-Host $http_host;
            proxy_set_header X-Forwarded-Proto $scheme;
            proxy_set_header X-Real-IP $remote_addr;
            proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
            proxy_http_version 1.1;
    }