Rossini continuo

When Rossini wrote his comic operas, what did he actually hear in his head for the continuo. We know that a number of Italian theatres continued to use harpsichords, though the last new instrument was made around 1800. And other theatres used a combination of cello and double bass, with the cello spreading the chords; this can be heard on the Naxos CD of The Barber of Seville. I've never understood why this isn't used more often.

But, the question that has always puzzled me is what Rossini expected; did he really want a piano. Would an early piano be what was expected, or would that be too exotic. After all, in the later 19th century one of the divas used to have a piano wheeled onto the stage during the lesson scene in the Barber and sing to her own accompaniment. So, if there was a piano on-stage, what was used in the orchestra?