Here are a piano concerto and a fantasy by Thalberg. Not that hearing them gives any insights to his ethnic heritage. Thalberg’s mother’s name was Stein, according to the bio, which could be Jewish. Otherwise I didn’t see any clues. It must have been a liberal age, since the different composers formed friendships and working relationships regardless of religion. Liszt and Mendelssohn, for example.
https://www.youtube.com/watch?v=tVtuqba4Wpg
https://www.youtube.com/watch?v=jxM9zoTaQRE
The Wikipedia article implied that Thalberg was really the son of the Prinz and Countess, rather than Mr. Thalberg and Ms. Stein, the parents of record.