Cannot connect QNAP NAS to airport extreme

doubt the new router should work differently

you can disconnect the router completley and its should still be possible for the mac to access the nas even without internet access that the router brings to the table.

if you connect the nas to the time capsule's switch ethernet ports the mac should be able to see it

you can also see what devices (ip addreses) are connected to the router using apples airport util

mine is the same

apart from my top is the tall airport extreme which has 1 old type airport express like yours and 1 new time airport express and the old flat airport extreme connected to it

my synology nas(wired ethernet) is connected to the old type airport express

but it seems that airport util only show wireless clients not wired ones, my nas show up under shared in the left side in finder and in synology assistant tool

if it was me then maybe I would try troubleshooting on another network maybe the nas is the problem rather then your network

My setup is a Zyxel router (with disabled WiFi) to which I have connected an Apple Time Capsule (wireless NAS server) and I try to make contact to my QNAP with my MacBook Pro over WiFi since my MacBook Pro doesn’t have a LAN port.

You disabled the Zyxel router's wireless radio, but did you also reconfigure it as a bridge? How about the Time Capsule? Is it configured as a router or a bridge. I am assuming that the Time Capsule is providing your Wi-Fi network ... correct?