It used to be so that pinned tasks in the icon-only taskbar would stay at their position once the task was launched (in the same way that windows behaves for example). In a recent update this behavior changed. Now the icon will move to the bottom (I'm using a vertical taskbar) of the list of tasks, below the other pinned-but-inactive icons. Once the task is closed the icon jumps back to its original position. Is this intentional? Is this a new optional behavior that I can control somewhere?

Adding a new icon-only taskmanager and removing the old one seems to have resolved the problem.

I have got the same issue.
Unfortunately removing the old icon-only task bar and adding new one cause another side effect.
When starting any application then additional (duplicated) icon appears on the right and disappears when starting finished.

Video: https://imgur.com/WURW21X