DT 3.9.4 here. I’ve never understood when the Activity pane is activated in the sidebar and when it appears (or doesn’t appear) as a standalone window. (When, for example a large scanned document is being OCR’ed to searchable PDF.) Where such “activity” is displayed seems to vary from day to day and task to task; if there’s a rhyme or reason to this it evades me. While the pane is a good idea vis-à-vis reducing on-screen clutter, I think, what I would really like is a preference setting that gives me the option of showing the progress of an activity in either the pane or the standalone window and, moreover, of keeping the window open until I choose to close it so that, should I switch out of DT3 to another app, the activity window doesn’t disappear. That would be very helpful for situations when I want to informally monitor something going on in the background, as it were, in DT3 while another application’s windows are in the foreground…
If the Activity window isn’t shown and a main window with the Navigate sidebar is open, it should show the Activity pane. If the Navigate sidebar and a main window isn’t open, the Activity window should appear.
Hmm. That makes sense to me, if I understand it correctly. But I just tried it – OCRing a long PDF document, only one main DT3 window open, no document windowsa open… and the progress of the “activity” didn’t show in either the pane or open the Activity Window, until I selected the latter from the Window menu. 
Was the sidebar visible? Does it work after restarting the app?
Yes, the sidebar was visible. And when I restarted the application and tried another long OCR job, the progress did load in the Activity pane, as expected. So my sense is that something goes wrong here if the app has been open for a good period of time. I rarely quit DT3, it sometimes stays open for several days at a time, as it’s one of my most used apps, and though I can’t be fully sure, my sense is that the Activity pane/window misbehavior is more likely to occur when multiple OCR jobs have been queued up. (And, in fact, another problem, though perhaps it is related (?), is if that if I queue up too many OCR jobs, say, a half-dozen or more taking several hours to complete, OCR will eventually fail, all pending OCR jobs will be teminated, and DT3 has to be restarted and the remaining jobs will have to be queued up.)
Running DT3 on an Apple M3 Pro MacBook Pro, Sonoma 14.2.1, 18 GB of RAM.
Does this happen e.g. after previewing video/audio files?
I can’t say, I generally do not open video or audio files in DT3.