Learn Italian: Questa sciarpa non è antiquata. Al contrario, è molto eccentrica! - This scarf is not outdated. On the contrary, it is very eccentric!

Al contrario (on the contrary) is a strong connector of contrast. It doesn't just introduce a different idea; it directly contradicts the negative statement before it (non è antiquata). It feels much more emphatic than ma or invece, stressing that the exact opposite of being old-fashioned is true.

Could I use the other contrast word from this lesson, bensì, here?

Yes, but you would need to change the punctuation. Bensì (but rather) is used to correct a negative statement within the same sentence. You would have to write: Questa sciarpa non è antiquata, bensì è molto eccentrica! You generally cannot start a brand new sentence with bensì.

Does antiquata mean the scarf is a valuable "antique"?

No, antiquata is a bit of a false friend here. It means "outdated" or "old-fashioned" and usually carries a negative connotation. If you wanted to say the scarf is a valuable antique, you would use the adjective antica (ancient/antique) or refer to it as un pezzo d'antiquariato.

Why isn't there a pronoun like essa before è molto eccentrica?

Italian drops subject pronouns whenever the context makes it obvious who or what is performing the action. Because questa sciarpa was just mentioned in the previous sentence, and the feminine ending of eccentrica confirms we are still talking about it, adding a pronoun here would sound clumsy and unnatural.