@ steep01 Thanks for your answer.
I made progress by using your link and https://forum.gl-inet.com/t/gl-x3000-routing-from-main-router-subnet-via-repeater-option/
It looks like this in Network → Firewall now:
I also added a route in Fritzbox (192.168.178.3 is the slate)
The Smart TV (behind the Slate) can access the internet now and uses the VPN which runs as OpenVPN on the Slate. The strange thing though is that there is no internet connection when I disable the VPN.
Another problem is devices behind the Slate plus can’t use DLNA but can ping 192.168.178.45. It seems that getting DLNA to work over subnets is quite hard.
The other way round is interesting too: If my phone is in the Fritzbox wifi, I can’t see the Smart TV to connect to the Youtube App. Only if I use the Slate wifi (being in the same subnet as the Smart TV), the smart TV is visible in the Youtube App.