I purchased a movie on Apple TV on a device and my smart tv only supports Apple TV and I can’t see my purchased movie on my smart tv

You still have the Apple TV App though, correct? There is not Apple TV plus App

In the Apple TV App, swipe or click left to bring up the side menu and select Library - Purchases 

Also, If your tv supports chromecast, you might be able to airplay from your iPad to your tv.

The App on my Smart tv is the Apple TV App. It has Apple tv plus in it. When I go to Apps that my cable box features it’s only Apple TV plus with a limited Menu, like what you’re saying yours is. There should be a way to install Apps you don’t have. I couldn’t find the Google Play Store on my tv . I had to use the voice command to ask for it to open. What tv do you have?