Figured bass question: When to use #6 in minor key?

Question

So I'm transcribing a piece by Giuseppe Valentini, one of his Allettamenti da Camera (1714), but my figured bass is a bit rusty. Here's an excerpt that illustrates my question:

So in the end of first full bar, it's pretty clear to me that the x over the G# indicates to play the #3 (B#), but what about the 5th? "The rule" (which can be found in Aldwell and Schachter, for example) is that the figures follows the key - however, in this case the melody suggests D# instead of the D-natural of the key. That chord is then forming the V of V (G# into C#- in the third measure), and maybe the next bar is just avoiding/extending that cadence or something.

But, that next bar does confuse me a little. The 5 6-slash over D# should be D# F# A B# (the 3 and 5 of the key with the raised 6), going to C# E G#, and then....I want to say the last two eighths are just outlining a G# major chord, but I just don't see it in the figure.

What I see is 7 over B#, which is B# D F# A (no modifications to the figure from key signature), and then X over G# is G# B# D (raised third, 5th in key). I guess if I was going to arrange that carefully, I would make do D B# resolving outwards to octave C#, but still...a much simpler solution would be to imply the D# here, making it another V of V.

So I guess what I'm asking about is the rule "the figure keeps the key signature" in minor keys, when the 6th note of the scale could be raised. How do you know when to raise it? What would they have done in 1714?

Answer 1

It's reasonably clear that what's happening harmonically is that a first inversion B# diminished seventh chord is moving through a passing-tone C# in the pass to a root position B# diminished seventh chord.

An experienced continuo player, seeing a 6-5 indication of a B# diminished chord, followed by a 7 over a B#, would recognize the change in inversion, so not need an explicit figure to sharp the D.