The Bach autograph on IMSLP shows...
...the mark above the
E is hard to see as a wavy line - it looks more like a long dash - but there isn't a sharp on it.
In terms of intent, I think the standard thing is to play the trill diatonically so that would be using an
In terms of music theory the clashing of the
F natural in the bass trill and the
F# in the treble is a cross relationship. Sometimes those cross relationships are avoided, other times they are exploited.
From an aesthetic point of view you can have two reactions: the dissonance is strong and upsetting, on the other hand it is strong and intensely dramatic.
The Harvard Dictionary of Music
A nice discussion of a very similar trill, but from the cello suites is available here...
Trills in the Bach Cello Suites: A Handbook for Performers
By Jerome Carrington
The part that catches my eye is: "...the prevailing concensus favors playing this trill without chromatic alteration..."