Learn Russian: Говорят, что это лучший пластический хирург в столице. - They say that this is the best plastic surgeon in the capital.

This is an indefinite-personal clause. By dropping the pronoun они, the sentence shifts focus away from specific speakers and instead highlights the general rumor or opinion. It translates naturally to 'they say' or 'it is said'. If you included они here, it would mean a specific group of people you previously mentioned are saying this.

Why do we use the neuter это instead of the masculine этот to agree with хирург?

In this sentence, это functions as a standalone subject meaning 'this is' or 'that is'. When used this way to introduce something or someone, it always stays in its invariable neuter form regardless of the noun's gender. You would only use the masculine этот if it were an adjective directly modifying the noun, as in этот хирург — лучший (this surgeon is the best).

Does лучший mean 'better' or 'best' here, and could I use самый лучший instead?

Here it means 'the best' (superlative). The word лучший can function as both 'better' and 'best' depending on the context, but the phrase в столице (in the capital) makes it clear that we are comparing this surgeon to all others in the city. You can definitely use самый лучший for extra emphasis, but лучший on its own is standard and natural here.

Is the comma before что strictly necessary?