[PROBLEM] WiFi (AP) and CAT-5 together

[psychofaktory]

I'm not sure what the issue is here. Are you saying there is ONLY LAN and no wifi at all in these locations and so there's no way to connect any "wireless only" device into the local network?

Yes, exactly this.

There are only a few wired devices there, such as smart TVs, that do not need to communicate with each other, but only need internet access.
And the smartphones access the internet via LTE.

Only to control Moode from the smartphones would a WLAN be needed.
And Moode provides an access point function as a matter of principle. Therefore, it would be unnecessary to purchase an extra WLAN access point just for this purpose.