I'd say Bar 4 is for vii°4/3, a.k.a. vii°7 in 2nd inversion. This interpretation assumes that the pattern of the previous 3 bars continues and the first melody note of Bar 4 is similarly the only nonchord tone in the measure. (Note that Bar 2 is actually VII6/5 or V6/5-of-III with that pattern interpretation.)
The first right-hand notes of Bar 6 are similarly also nonchord tones - all 3 of them are suspensions in this case. (The right-hand notes of the second half of Bar 6 are problematic - the best I can come up with is that Bar 6 is harmonized as VI7 and that the last right-hand notes are nonchord tones: anticipations of the starting right-hand notes of Bar 7.)
I know of no name for either the bassline or the chord progression beyond "ascending bassline". I don't previously recall hearing such ascending basslines in Baroque music at all, but then I'm kinda terrible at hearing basslines.