Someone gave me the tip (thank you!) to use VLC to play YouTube videos with my Chromecast. Although it is possible to stream YouTube videos directly in the VLC Android app itself, it somehow doesn’t work in combination with the output to the Chromecast. An alternative is of course to first use NewPipe to download a video and then play it on the Chromecast using VLC.
However, I have now found another possibility. In Windows, you can also use Microsoft Edge to stream YouTube videos to the Chromecast. There, they are not opened with the YouTube app (which constantly shows me ads), but only with a video player. I have now tested this with a few videos and did not see any ads. Whether uBlock Origin also plays a role in the Edge browser, I have not tested.
Update: I came across SmartTubeNext, which does exactly what I want. YouTube Premium and Premium Lite are not options for me, as Premium Lite is not available in my country and I don’t need the music in Premium, as Deezer is my music streaming service of choice.