Bwv anh 114 is based on two-part harmony. I have heard that this is bassically just basso continuo. How is this basso continuo if it has only two voices? The books on basso continuo talk about four-part harmony. Is this perhaps a special style of basso continuo?
"I have heard that" isn't a reliable source, especially if you don't give a reference to where you heard it.
In any case, there are thousands of 18th century manuscripts which obviously do have continuo parts, but no figures. Musicians were expected to be intelligent enough not to need to be told the obvious, if the harmony was as straightforward as Bwv anh 114. There are also thousands of 18th century scores where the figured bass is so full of errors that presumably the performers just ignored the mistakes and couldn't be bothered to correct them on the copy!
The books on basso continuo talk about four-part harmony
Modern books (which use figured bass as a dead language for teaching four part harmony) usually only talk about four part harmony. 18th century books (e.g. C P E Bach's "True art of playing keyboard instruments") talk about playing different numbers of parts and how to decide how many parts are most appropriate, and also about improvising multi-part imitative counterpoint, not just playing block chords with the right hand and the bass line with the left.
Since these pieces were used by J S Bach as teaching pieces, if he wanted to teach somebody to improvise harmony or counterpoint without figures as "training wheels", there wouldn't be any figures on the manuscript!
The practice of basso continuo has its basis in two part harmony, namely a bass line underpinning a melody. However, musicians would then interpret the music by so-called "thickening" the bass, filling in the harmonies between the bass line and the melody.
I would liken the process to giving a speech from jot notes. I could have notated (for myself) the first para above as
B.C. based in 2 parts: bass below melody. Musicians interpret by "thickening" bass <-> melody
However, in interpreting those jot notes, which transmit the entire idea already, I need to make them grammatical (for instance by adding "the" and "a") as well as to make them compelling, with nicer wording. That is the analog of interpreting the continuo part.
During the baroque, several trends happened.
While most notated music was intended for just one-time use, a greater sense of "writing it down for future use" (even posterity) began to develop.
Rich improvisation, by individuals and ensembles, flourished, and then became excessive; musicians outdoing each other in realizing, thickening, ornamenting, with more enthusiasm than skill, and obscuring the composer's intentions rather than bringing them to life. Just like someone could speak from my jot notes with horribly overwrought language, and misinterpreting my intentions.
Rules and practices for harmony, both for performers and composers, were written down. That's where the rules for four-part harmony come from, and the exercises with it that composers and music students study to this day. Theorists and composers found four voices was just enough to get across harmonic ideas, with enough flexibility for creativity, and expounded on how to do it.
These 3 trends are not consistent, of course, though also reacted to each other. So musicians were trained in harmony based on four part principles, but would often realize basso continuo parts with more or less than that, and it may or may not have met the composer's intentions.
J. S. Bach was a genius, though an old-fashioned one, continuing in the baroque style (arguably better than anyone else) when musical fashions had moved on. In his chorales (and elsewhere) he was outstanding at realizing 4 part harmony with beauty and restraint. And in much (all?) of his music, he wrote out his harmonies and ornamentation, not leaving it up to performers to improvise and muck up. Like someone might write out a speech in full sentences, not jot notes, either so they don't need to think hard to interpret it, or so others reading their notes don't misinterpret them. And the performance practice has continued to this day that performers "don't muck with Bach", i.e. don't thicken his written harmonies or ornament his music lines, while they do (and generally must) do so with his earlier, some would say 2nd rate, baroque peers.
And so "the Bach minuet" BWV Anh. 114 is generally learned, and played, just the way it is. It becomes an interesting theoretical or pedagogical exercise to say "how could the harmonies be thickened in line with basso continuo performance practice of the time?" and "how could a 4 part harmonic and contrapuntal structure in line with the treatises be wound around the notated melody and basso lines?", related but not identical questions. But it is generally assumed to be intended to be played just the way it was written down.
The question becomes more interesting since I believe it has been established that the minuet in question was not actually composed by J.S. Bach, just written down by him (in a notebook for his wife). It was actually written by a certain Christian Petzold, a (to us) poorly known but (then) well-respected organist and composer. And so perhaps "rules" like "Bach wrote what he wanted, don't add notes!" maybe don't apply.
However, regardless, the logical sequence "Bach wrote this so it's meant to be played exactly as is. It has 2 parts. B.C. is supposed(?) to have 4 parts. Something's wrong" has a number of fallacies in it. Not egregious ones; just several instances of speaking in absolutes rather than general simplified principles.
Basso continuo is really just a description of the bass part. If a bass is labeled as continuo it doesn't indicate how many other parts are included. You could have continuo with a single part like a baroque violin sonata or two parts like a trio sonata.
Lots of music with basso continuo is two parts only. Actually, I think of basso continuo with only a single line above as one of the commonest forms of writing and the essence of homophonic music: bass plus melody with inner voices as harmonic filler.
The reason there are only two parts is because the additional "voice" that would make complete four part harmony were considered harmonic filler.
You can reduce any piece (or many pieces) to b.c. or also extend any two part or one part music to 4 voice b.c.
Why do we ask, how Bach meant this Menuett? A lot of his writing has a pedagogical intention!
Mind what Bach himself has made with the church chorals or with the concerts of Vivaldi and other composers. This material is free to use and how you will interpret it is up to you.
You can play the 2 part inventions in full harmony or as 3 part inventions, or play the Cello suites on piano in full chords, or play a violin concerto like a 2 part invention.
Also mind that figured bass studies often give you just the bass line and you have to create an interesting 2nd part or a setting of 4 voices with an interesting melody.