In the Krita manual, it says you can draw a circle by radius by holding the [ctrl] key when drawing the circle. Whenever I hold the [ctrl] - either before drawing or after I start - all I get is the "color picker" function. Is this a bug? I'm using Krita v4.0.0 with all defaults in place.

You have to start drawing the circle first, then hold down the Ctrl key. That should get it to do what you want.

You can also press the alt key after you start making the circle to move it around

You can also use the Shift key as a modifier to force the drawing of a circle (not an ellipse) and this can be used at the same time as the Cntrl key to give you a true circle dragged out from the centre. If you do that, it only responds to vertical cursor movements.

If you use the Shift key after you've started drawing an ellipse, it will be forced to become a circle.

It's interesting to experiment with the various combinations at different stages in the drawing of an ellipse to see what effect they have.