Thanks! This indeed brings back the stats page.
Just for my understanding - why does it work? My assumption was that the router's 192.168.1.1 is at the same time the localhost 127.0.0.1...
127.0.0.1 is a separate virtual loopback interface that is always up and running regardless of the state of the other interfaces in the system. It is used by the device to communicate with itself - mainly for diagnostics and troubleshooting or to access services running on the local machine.
If you want to access a service using the loopback interface, the service must listen on that interface.
In your case, you have restricted tinyproxy to only listen on the (physical) lan interface, so it was unreachable via the loopback interface.
AFAIK listing multiple listening interfaces is not supported by tinyproxy, so the only option is to allow the service to listen on all available interfaces