I would be inclined to describe the texture as chordal - meaning that it really emphasizes harmony above any melody lines. It is somewhat difficult to classify the music with the terms you list because of this.
First, it is worth noting that your copy of the score is somewhat different than what Bach wrote; this edition (edited by Czerny) is more faithful to the original. Here's what the start of that score looks like:
The difference between this score and yours is that the attacks (i.e. when each note is first struck) is the same, but notated with sixteenth notes rather than eighth notes. However, in this score, you are asked to hold the bottom two notes, rather than just play them. In particular, this means that the melody is accompanied - and that there are definitely multiple voices.
However, more to the point, we can explain how this prelude is put together in a simple way. The form is known as a figuration prelude. Basically, how this works, is you start with a chord progression. The five measures above correspond to the following five chords:
Then, to make the prelude, Bach just plays the notes of the chords in a consistent pattern. In this prelude, he just plays the five notes of the chord from bottom to top, followed by a repeat of the top three notes - and then repeats the whole figure. This is the case for all but the last two measures. In a sense, all that the music is is captured by the chord progression and the first measure - since you can recreate it from that. This is why I call the music chordal.
At the end of the day, there is a degree of polyphony here. Note that every chord has five notes in it. We can regard the series of bottom notes as forming a voice - and we can regard the series of top notes similarly and so on - giving us five voices. The reason this is productive to think about is that Bach follows a practice known as voice leading to put together the chord progression.
The basic precept of voice leading is that voices should not move more than is necessary - and you can see here that, if you trace any voice through, there are very few leaps. In a sense, each voice in the chord progression acts like a melody - but Bach makes everything so smooth that it would be somewhat absurd to claim that any of the lines constitute a meaningful melody alone. In this sense, the music can be said to be polyphonic - but this obscures the larger harmonic structure of the music. Note that this also decidedly classifies the whole piece as homorhythmic because the harmony changes every measure (or every two measures in your score).
This is all to say that, if we adopt this view of the music, we find that the structure is best classified as coming from a chord progression rather than from a stack of melodies. Of your terms, we would most productively argue that the music is polyphonic understanding the underlying structure. However, this requires more analysis than simply looking at the score. More or less, the moral here is that, in music like this, "voice" doesn't just mean a member of a simultaneously struck chord or a separately noted line, but can rather more generally refer to a line that is somehow underpinning the music.
Of course, one could argue that the music is monophonic without doing all this analysis - and this reading would have merit (because, for the performer, the melody really needs to sound nice, even if it is just an articulation of an underlying structure). I just want to point to the fact that these classifications are kind of fuzzy in music and that there are multiple meaningful interpretations of such a question.