Unfretted clavichord also works very well for them. IMO even better than the harpsichord, the sound is less grating. There are a few bits that aren't playable on the fretted clavichords of Bach's day, but very few and it can be performed on these (and probably was given how common they were).
There's also an excellent performance on the organ[1].
Clavicord was definitely the virtuoso instrument of the period. It allowed for a lot of control, more than a modern piano. Its biggest issue, lack of sound, made it great for students like the ones Bach addressed in Clavier.
The strings in clavichords vibrate from the bridge to the tangent (the metal hammer that strikes the string), the remaining distance to the tuning peg is covered in damping felt and so does not contribute to the sound. On a "fretted" clavichord, several notes strike the same course (of two strings) at different positions. Only one note can play at a time on each course, so some combinations of notes aren't possible. Unfretted clavichords have a course for each note, but weren't at all common in J.S. Bach's time.
There's also an excellent performance on the organ[1].
[1] https://www.youtube.com/watch?v=mBQxfv7IZWA