In reality, smart TV's aren't smart, they have an app to access content some smart tvs have better apps.
Ask Ring and or Samsung, either directly or there own consumer forums.
Ring being an amazon product, may be accessible if there is an alexa app.
sometimes think an android box/ plugging your phone in is more cost effective if the Tv can handle that, as smart tv's may or may not support latest versions of apps after a while, then a TV can be an expensive thing to update, whereas a decent android box is relatively cheap.
Don't know if it would help but you can buy tiny PC's for less than £100 on Amazon.
Presumably you could run the app on a PC and have it connected to the hdmi of the TV.
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