In "Girl Genius" novel "Agatha H. and the Clockwork Princess", do the Van Rijn Muses contain human consciousnesses?

There's too much we don't know about the Muses to answer fully.

Let's discuss your thoughts first.

"Anevka", the robot clank that Tarvek's injured sister operated, was a learning machine that adapted to how it was used, and didn't even realize the original Anevka had died at some point during her operation. Tarvek built it himself, based on what he learned from studying the Muse Tinka. Lucrezia also used this same clank, albeit by getting downloaded into an improved head Tarvek had built.

This suggests Muses either can host or can mimic human minds... but doesn't really prove it, given the tech is Tarvek's, "Anevka"'s lack of self-awareness, and Lucrezia's lack of... well, anything resembling humanity. Does make it pretty likely.

Second, we absolutely know that minds - synthetic or organic - can be transferred.

Lucrezia's studies under Castle Heterodyne made concrete that minds could be transferred. Lucrezia was able to transfer the original muse Otilia's clank mind into the organic (mostly) construct Von Pinn, and then transferred the Heterodyne Castle AI mind into Otilia's clank body. Note however, her work isn't without effects, intentional or otherwise. Otilia-in-Von-Pinn's mind was a few fries short of a happy meal by the time of the story, probably not helped by being beholden to Lucrezia's control voice which the Von Pinn body had built in. There's also a really giant question mark about if the Castle AI got forced into Otilia's body, whether or not that was relevant to what the hell happened that wrecked Castle Heterodyne to begin with - which definitely broke whatever mind was left in the Castle.

In addition, we have a hearsay confirmation at a point you haven't read yet -

Finally, the Muses themselves.

• Moxana. There seems to be very little point to Moxana's lack of speech. Sure, it forces her metaphoric communication to be more effective, fitting her role. But if Van Rijn's clanks truly were original creations meant to be a pinnacle of form... where exactly did the idea of being mute come from? None of the others were, and the ones we've seen weren't meant to be great orators.
• They did serve the Storm King, but were built to inspire him to greatness, not purely to obey him. ... pretty sure it didn't work. All spoiler at this point.