Apple TV issues with a Purchased Show

Hi Everyone! 

Recently I purchased The Great Season 3 on my AppleTV app through my phone because I can’t access it through Amazon Prime in Canada. Figured this would be way easier as I had an Apple Subscription in the past.

Unfortunately when I go into AppleTV+ app on my Samsung Television there’s no option that shows my library. Cannot find what I’ve just purchased. Why is that? There should be no reason why my purchased movies don’t show up in the App on my television yet they show up on my phone. Apple needs to fix this.

There’s no chrome cast button on Apple to connect to my tv, there’s no way to screen mirror because it says I’m recording and stops playing the show. I’ve tried Apple Air Play on my TV and although my TV is a smart TV from 2017, it’s not compatible with Airplay. Tried downloading Apple TV on my Xbox one with no avail, it wasn’t there. 

Is it possible to update my tv and for Apple to make Airplay available on it? The model number is UN55MU6300F it’s a Samsung Smart TV. Also have a Sharp Roku TV 5303X. Though I can’t find either of these listed on compatible Air Play Televisions. 

I’m so upset that I can’t just access my purchases through the AppleTV app on my television. Feels like I just wasted $20 and a lot of my time trying to set it up. Would’ve been more worth it to spend $35 and buy the physical form.

If you have any advice or information that would be useful please let me know. Really need this to work on my TV as I want to watch it with the family, not just on my phone.

Thanks

Emily