> Is my impression correct, that in general "the {thing}" is a noun phrase without implying anything about {thing} itself?

Yes, with some minor caveats:

1. Some people prefer to see "the {thing}" as a 'determiner phrase', where 'determiner' is the name for the part of speech to which the belongs. You can call it a 'noun phrase' without losing anything meaningful. 'Noun phrase' is definitely a better term if you're not deep in the technical weeds of grammatical analysis.

2. There are conclusions you could draw about {thing}, but they're more complex than "it's a noun". It's fair to just not talk about them.

3. In language, there are always problems somewhere for any analysis. (Which is why an unbroken chain of transmission can have Latin on one side and French on the other.) I wouldn't even say that a noun phrase with that structure exists at all in an example like "The more you say it, the more I think it". But that particular construction is weird enough that I'm perfectly comfortable saying it's just outside the scope of your qualifier "in general".