I have tried this, but unfortunately, it did not work. I have tried this suite of commands

login.router.lan {
    reverse_proxy 192.168.1.1:80 {
        # Preserve original host and scheme
        header_up Host {upstream_hostport}
        header_up X-Forwarded-Proto {http.request.scheme}
        header_up X-Forwarded-Host {http.request.host}
        header_up X-Forwarded-For {http.request.remote.host}

        # Keep cookies intact
        header_up Cookie {http.request.header.Cookie}
        header_down Set-Cookie {http.response.header.Set-Cookie}

        # Preserve Origin/Referer for CSRF tokens
        header_up Origin https://{http.request.host}
        header_up Referer https://{http.request.host}{http.request.uri.path}
    }
}

Info: My caddy uses HTTPS but the router login page is HTTP. Not sure if this is relevant.