Apple Music doesn't work via WiFi.

Hi.

So, We have an Apple Music Family subscription. There are several devices with several Apple IDs.

I have two separate WiFi networks, one of them directly from the Router, others via a few Airport Extreme stations. Both networks each have 2.4GHz and 5GHz variant (so four SSIDs in total).

Devices in question are: iPhones: X, 7, 6s, 2x SE, 5; iPads: 2019-WiFi only, Pro 1st Gen 12.9, 4th Gen.

Apple Music refuses to work if only WiFi is connected.

More specifically, Apple Music refuses to PLAY songs via WiFi. I can search and browse through all the content and it works, but if I tap Play anywhere: The song name appears in the bottom bar, then it takes couple of seconds and then displays the error "The network connection was lost." And displays an "OK" button.

This is with any of the available networks.

The Router is a ZTE MC801 5G router, that works in "4G+" mode currently (as there is no 5G network here, it just happened to be the best 4G router from our ISP that was available and only a few bucks more than a 4G-only model, so I went for that). Router itself is in NAT mode, Airports in bridge mode. So the Router works as the DHCP on the network.

What could stop Apple Music working? Everything else seems to work perfectly, App Store and internet in general work just fine - same with all games that require internet connectivity. It appears only Apple Music doesn't work and ONLY the playing of songs in that even. The app works in other parts just well.

Apple Music/iTunes DOES work on the same network on a Windows computer (connected wired to the Router though - not via WLAN).