OK, so I lost a huge amount of progress, but I did find a way to “fix” this bug.
I went to an old saved game and completed the tasks in this order:
- Brewed remedy
- Talked to Matthias
- talked to meclichar.
- Administered the remedy to the ill, including the prisoner
- waited
- Interrogated the prisoner
- Sent prisoner to Rattay
- Talked to Radzig.
Unlike my first attempt, this did trigger a cutscene and the quest moved on.
What did I do differently the first time? I think the big issue is that I left talking to Matthias a bit too late. I did it probably after I brewed/administered the cure and talked to Melichar.
So my hunch is that, to avoid this issue, talk to Matthias as early as you can.