Firestick would be an option for sure, just make sure it is one of the models listed from the link I posted above. I wouldn't advise getting a 2nd gen Apple TV as that is 9 year old hardware, obsolete, and would not have access to the TV app. The 3rd gen is still being supported and has access to a server version of the TV app, as that model does not run native apps. So if you did find one on the used market it is your choice as to whether you consider it.
Completely understandable about wanting to avoid losing app compatibility, though of the few that I had I found alternatives quite easily so you may want to look into that so that you can then upgrade the OS. In the meantime, as I said you can use the website to access the service.
Yes, I wasn't debating that yours was a smart TV but that it would need to be compatible with the app. Smart TV platforms are notorious for short lifespans, Samsung for example has the TV app but chose to leave out models sold earlier than 2018.