I have found this interesting post on androidpolice.com https://www.androidpolice.com/2019/09/01/how-to-fully-control-youtube-on-your-tv-from-your-phone-wit... in order to optimize the use of youtube app from a smartphone to an Android TV.
It explains the differences between the two possible options and the better features you have using "Youtube on TV" rather than simply casting. It seems much better to me (except for the fact that you cannot switch on the TV automatically like with casting)
