My ip information website now immediately shows both your IPv4 and IPv6 address, if available.
This was made possible, by adding two subdomains (v4.ip.zuim.de and v6.ip.zuim.de), which only have a DNS record for the respective IP version. This forces the browser to use the specified protocol without relying on directly accessing the server by its IP. This is important, because using the addresses directly would not support https.
Now everything is sent over https!