> you have zero privacy

Is this data linked to me personally in some way (e.g. though an account) or is it anonymous data?

They can definitely work out who you are from your IP address. (or get close enough that the advertisers don't care) Not too many people are putting a VPN on their router and using throwaway accounts for their smart TVs. This might be difficult anyhow if your log into major services such as Amazon, etc, who will know who you are.

I'm not saying this is impossible to avoid, but it ends up being a LOT of work when the alternative is just not connecting the TV to the internet and using a laptop / Apple TV / etc. instead.

Personally identifiable. Most smart TVs force a login to connect to the Internet or even use at all.