Admitting I haven't used the TV app very much. But the way I would look into it is to try setting up a timeout routine first. If that doesn't work, Miracast to a display that has a sleep timer and rely on that. Although if you have a Samsung TV, casting through your phone is an extra step.
You might be able set a routine for it - if <app name> open, then add conditions or timer for when it stops. You'd have to play with the routine settings to see which works best. But you can set a timer to start when the app opens, select the time, and then select the app to close. You can also add the condition for it to do those actions during a specific time period or in a specific place.
I have a surefire fix for that, though. If I'm sleepy, I don't watch anything on the phone, and if what I am watch is boring, I turn it off (even though I'm the type of person who mostly has to watch things to the end, no matter how bad they are)
