Thanks for the suggestions Adrian, Daniele!
I have been fiddling with the resolution and different TVs, inputs etc, it turns out that sunrisetv.ch does not currently (and since a few months) like the Safari browser, even though it is kept up to date on the system. The playback of video from the website works with Firefox. To note that with Safari, all streaming works with screen mirroring, including the Home screen of sunrisetv.ch, up to when I select something to play, which is when the screen goes black both on the laptop and the TV, while audio works. For me, it is much handier using a browser than adding apps, considering my use of this feature is occasional.
Thanks again for helping, the issue is solved.