Lighttpd

I'm trying to use mod_auth for managing authentication on a Lighttpd server (version 1.4.48) before sending the HTTP request to an underlying application and I need that Lighty sends to it the username of the authenticated user. I thus put the following data in my Lighty configuration:

proxy.forwarded = ( "remote_user" => 1 )

Unfortunately, it seems that the option is ignored. Here is a netcat output that dump my HTTP request on the underlying application:

GET / HTTP/1.0
Host: cal.example.fr
Cache-Control: max-age=0
Authorization: Basic c3B5ZGVtb246dGVzdA==
Upgrade-Insecure-Requests: 1
User-Agent: Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/68.0.3440.106 Safari/537.36
Accept: text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,image/apng,*/*;q=0.8
Accept-Encoding: gzip, deflate
Accept-Language: fr-FR,fr;q=0.9,en-US;q=0.8,en;q=0.7
X-Forwarded-For: 192.168.1.11
X-Host: cal.example.fr
X-Forwarded-Host: cal.example.fr
X-Forwarded-Proto: http
Connection: close

For testing purpose, here is a minimalist Lighttpd configuration file that you could use for reproduce the issue:

server.modules = (
    "mod_auth",
    "mod_authn_file",
    "mod_proxy",
)

server.pid-file = "/run/lighttpd.pid" 

server.bind = "0.0.0.0" 
$SERVER["socket"] == "[::]:80" {  }
server.port = 80
server.document-root = "/var/www" 

auth.backend = "htdigest" 
auth.backend.htdigest.userfile = "/data/htdigest" 

auth.require = (
    "/" => (
        "method" => "basic",
        "realm" => "example-web-radicale",
        "require" => "valid-user" 
    )
)
proxy.forwarded = ( "remote_user" => 1)
proxy.server = (
    "/" => (
        "application" => ("host" => "10.0.3.11", "port" => 5253)
    )
)

Thanks for your investigation.