Thanks to @ff2u who originally pointed out this issue (on my request, I only signed up for this forum a couple of months later). In the meantime I had switched to Clock | F-Droid - Free and Open Source Android App Repository which didn’t suffer from these small bumps in the road and used it ever since.
However, now that I upgraded to Android 12 and inspired by Which preinstalled app do you really use? I had a look at the default clock app again and found that it has improved in both the seconds|milliseconds and the minutes|seconds|milliseconds display:
For comparison, the Deskclock app:
I have gotten used to Deskclock quite a bit by now, but I can say that at least the default Clock is more competitive with me now. Will see if I stick with Deskclock or go back. 
P.S.: If you folks wonder why the hell someone would care about the stopwatch in panorama view … I’ll just say it’s good assistance next to the bathroom sink 2-3 times a day 