IpTV and alternatives...

The Chromecast stick only streams content, a stick that allows you to install apps yourself is better.

No, there are tons of Chromecast apps nowadays. And basically, you can stream almost anything to the Chromecast. But for that, you'd need another component to send the content (a tablet, for example).
In any case, it would be good to have a device on the TV where you can directly install the EWE app. I agree with that too.

Well, I always say, you won't get a brilliant picture and program variety cheaper or easier than with a SAT dish.

You really don’t need that stuff. Satellite dish on the roof. Plus a decent internet connection, and you stream your content through the various providers on the market. The important thing is to have LAN access at the TV. Then you don’t need any boxes or other restrictive contracts.

By the way, we currently only have a 6 MBit connection. But we can easily stream Premiere GO or access our favorite episodes via the media library.

What use is LAN without the app that plays it, or is it enough to create a bouquet with IP?

Many TVs have this integrated or you set up a small media center, with which you can do everything at once and be free.

I have been through a lot in recent years, first my brother raved about Premiere GO, then my neighbor said there was something from Premiere. Then he didn't find it so great again. I don't like hardware that restricts me, whether in quality or possibilities, I want to be free. And when we're bored, my wife opens a web browser and we watch Bares für Rares. All without additional costs or contracts.

We have had Entertain for over 5 years and are thrilled. However, we also have a 50mbit connection, so you can watch HD and record at the same time. If you want the big paid provider with three letters, you don’t need an extra receiver, because Telekom integrates it with all the advantages of the Entertain receiver.

With 16mbit, you can really only watch HD but not record at the same time. For me, that would actually already be a deal-breaker...

One small note. If Telekom offers you a 16mbit connection, they also guarantee you that data transmission speed. As you already wrote, the local provider BIS offers 50mbit. You definitely have to look at the fine print to see what minimum they guarantee, maybe you’re not even that far from 16mbit...