You can't record YouTube videos via your telly but you can using a computer. (Instructions on request but it would help to know which web browser you use on your computer).
You can do it on the computer. If it's a past broadcast video, some video downloader software like HD Video Converter Factory Pro or 4K Video Downloader can help download the full-length video. For the live streams, try to use some video capture software like OBS Studio, ShareX, CamStudio, etc...