Very nice-
I imagine the piano's construction has a classical construction to it, no? Is it a type of piano?
In the video of Handel's sonata for recorder and basso continuo in a minor, the continuo is being played on a harpsichord. Despite the physical similarity, it isn't that much like a piano - it is a string instrument, much more like a guitar than a hammered instrument like the piano.
The instrument that Mozart, Beethoven, and even Schubert knew was not the Steinway grand that we picture today. Mozart's instrument was likely a proto-type piano, known as the forte-piano. The instrument was not capable of much change in dynamics and had either no or very ineffective damper pedals.
Schubert's unfinished sonata in f-sharp minor on forte-piano:
Beethoven's immemorial moonlight sonata played on a fortepiano:
(Note that it looks almost indistinguishable from a harpsichord; the tempo may seemed rushed, but the instrument is simply incapable of the languishing melodramatic agonizingly s..l..o...w... tempos that moderns indulge in)
This on the other hand is a harpsichord: