Happy with first image.
Second image seems to show the controls for a picture.
I can use the select Tool and then click the Show rotation centre icon for the CoR to appear.
I can move it anywhere.

I just click on and click off and on again and the CoR is centred to the shape or group.
Selecting just one shape and the CoR remains in place.

There is the one visible helium balloon on a string control for both shapes and images to click and move to rotate about the centre.
The hidden others appear on a close hover to the corner controls.

If it is not working as I describe then try a Run as administrator the once.

Thanks for the effort to capture what you are experiencing.

I am using the same version.

Acorn