Though the extent of it really matters, I always hear "Norway is a capitalist country" when their economy is primarily in the hands of the state, more than for example Venezuela.
But people tend to point to Venezuela, and not Norway, as an example of a failed state owned economy.
It's not really about "sectors" of the economy that are publicly owned but actual economic output. The money in the US is produced and it is in the hands of private individuals most of it. In Norway near 70% of it is produced and in the hands of the state. Obviously Norway is a particular example because they're a country that relies on natural resources extraction. But you can look at other similar countries in terms of their exports (Australia, Chile) and see how the Norwegian model differs.
The USPS, for example, is a service. It's not really a business, it doesn't have to be profitable it ideally has to be sustainable but I wouldn't say it's a necessity. Not only that, it subsidised private businesses like Amazon.