Okay, got it. www.econda-monitor.de is showing the blocking page.
Just to summarize (e. g. for other users facing similar issues / having similar setups with other web services running on the Pi-hole Pi):
- Using a second IP address is the basis for a clean service separation (not only but especially when your other web service is running on ports 80 oder 443).
- Don't forget to set the same IP address as lighttpd uses for Pi-hole/dnsmasq. Easiest way is to reconfigure Pi-hole (pihole -r) and say NO to "do. you want to use the current IP settings as static IP address for Pi-hole?" and specifying the right IP settings.
- There are several places to check and/or edit when using two IP addresses:
a) Lighttpd/Pi-hole Webserver config file
b) nginx/other webservice webserver config file
c) /etc/network/interfaces and/or /etc/dhcpcd/dhcpcd.conf files
d) Browser Bookmark for Pi-hole
e) /etc/pihole/adlists.list IF using additional hosts file (e.g. http://localhost/adhosts.txt where localhost needs to be changed to the lighttpd IP address)
f) Router port forwarding in case your other web service is provided to the internet
g) Router config for DNS server (hardly depending on how the Pi-hole DNS service is distributed to the clients - in my case the router points the clients to the Pi-hole) - I'd also like to highlight I only use IPv4 and disabled IPv6.
So there are a few things to keep an eye on but at the end it's absolutely possible to run Pi-hole next to other web services on the same Pi without negative impacts.
Thanks to @Mcat12 and @deHakkelaar for their excellent support on this.