One of the earliest self-playing musical instruments was
a harpsichord, or at least a member of the harpsichord family.
This was a keyboard and barrel operated spinet made around 1625
to 1650 by Samuel Biderman of Augsberg.

This is a small 'octave spinet' of three octaves with twenty notes
being played by the pinned barrel.  The barrel was operated by a
clockwork motor and the barrel was pinned with four tunes.  This
instrument was included in the recent 'Royal Music Machines' exhibition
at Utrecht, and was loaned by the German National Museum in Nuremburg.
A number of similar instruments were made around that time, including
one for King Henry VIII.

The spinet is a member of the harpsichord family in that it employs
a plectrum to pluck the string.  The spinet is generally smaller than
the harpsichord and only has a single rank of strings whereas the
harpsichord can have up to three, or even more in exceptional
circumstances.  An octave spinet is a small portable instrument made
to play an octave above normal pitch.

Many years ago, the British automaton maker David Secrett built
a small run of lute players which included in the base a barrel
operated plucked string instrument rather than the more usual musical
box movement.

Another self-playing plucked string instrument is the Wurlitzer harp.
This is more a harpsichord than a harp in that it employs jacks with
plectra and dampers.  I have never heard one sound remotely like a
harp.  It's more like a harpsichord being played by an incompetent
pianist playing music totally inappropriate for the instrument.  The
Wurlitzer harp could sound half decent if someone were to arrange some
sympathetic music for it.

I do remember seeing a photo of a real harpsichord that had been
modified to accept a bank of solenoids.  Unfortunately, I cannot locate
this in my library.

So in answer to Brian Smith's question, yes, self-playing harpsichords
have been around for longer than self-playing pianos -- much longer.

With best regards,
Nicholas Simons, GB