There is nothing wrong with the setup .. the IP addresses and everything are fine.
You have discovered the bug in the Apple router. It simply fails to work properly with some modems. We don't know why.
This issue is seen most clearly with SB6121 and SB6141 modems but it happens on lots of modems particularly cable modems. And yet it doesn't affect everyone.
Our usual recommendation is to replace the modem.. some models work fine.. like in the US cable providers the Zoom models work fine. Where I live the ISP provide a modem and you cannot replace it. That makes that solution impossible.
So you MUST replace the TC as the main router.
Andbefore thatthere was a router D-Link, too, everything was fine (
You need to go back to using a different router. The TC can still work fine as a backup target for Time Machine and a Wireless Access Point but you cannot route through it.
We did suggest to people in the past to use a 10/100 switch between the cable modem and the Apple router.. that sometimes fixed the problem. Or a cross over ethernet cable. that also fixed the problem for some.. but in neither case did it fix the majority of issues.. so in the end we changed the recommendation to simple replacement.
Apple has no fix.. to this point they have not acknowledged there is even an issue.
You can get the TC replaced under warranty but the replacement will probably be no better. And even if it works ok at first it seems the problem can return at any time.
So replace the TC as the main router is the best solution I can offer you. Plug the TC into that router by ethernet and bridge it. The router you use does not have to be expensive.. in fact buy one that takes a third party firmware like gargoyle is well worth the effort.
Just google for gargoyle firmware. I am not allowed to post more info.