iPad sidecar touch bar doesn't respond in clamshell mode

I'm using a 2018 Macbook Pro 13" (which has the physical touch bar) in clamshell mode with an external display, and would like to sidecar my iPad for drawing or other tasks. I'm currently running the latest version of Sonoma. I also would like to be able to access a virtual touch bar on the iPad, since there is no alternative method of getting a touch bar.

Unfortunately, while the virtual touch bar on the iPad shows up and updates according to what application is open on the sidecar display, it is not responsive whatsoever to touch or Pencil unless I open my laptop, in which case it works perfectly. (The sidebar works as intended whether or not the laptop is in clamshell mode, so I believe this is a bug related to the physical touch bar.) This completely defeats the purpose of the feature for me, since if the laptop is not in clamshell mode I could just use the physical touch bar on the laptop. Is there a workaround for sidecar with touch bar laptop models which don't require opening the laptop? Maybe some way of performing a hard reset of the virtual touch bar? I've tried disconnecting, reconnecting, changing other sidecar settings, etc.