On Apple Watch, dictation is done by watchOS. Apple does not provide APIs to integrate directly in apps like is possible on the phone…so, Drafts is limited by the timeout Apple applies, which is around 30-60 seconds. More details on the implications of this limitation prior thread.
Essentially the app says to watchOS, “hey, I would like text input” - then watchOS takes over, and Drafts is not involved until you are done (whether dictating or typing or scribbling, whatever), you press the “Done” button, and watchOS should hand the result back to Drafts.
That said, it should stop listening, and allow you press “Done” and pass back what it did capture. What you describe sounds like a return of a watchOS bug that was around for a while 2 years ago, but Apple fixed. As described here:
If you could answer the questions in that thread, I’ll do some testing here so I can report this to Apple.