Apple TV HD, tvOS 9
Do you have the Apple TV box? If this information is accurate, then you would need about 5 years of updates! We’re on software tvOS 14.7 now. Update your Apple TV - Apple Support
Apple TV does not have queue or My List where I can save shows I want to watch later.
The Apple TV app on streaming devices does have a queue list. It’s called Up Next, and it is featured prominently in the Apple TV app.
It is true that the Apple TV+ website doesn’t have that same functionality. The website is also smaller in scope, compared to the Apple TV app on streaming devices, as the latter can also include a mix of iTunes Store movies and other Apple TV app Channels.