This probably has something to do with Layers as if it is imported as Layers it displays this issue and when imported as Image it works as expected.

Maybe I need to better understand layers.

Does that help anyone to point me towards understanding this behavior when imported as Layers?

Should have nothing to do with how the image is assembled.

A few strange things happening with your set-up, however ref: the screenshots.

1. You are on the layer you need to rotate. Note if the layer is not visible the rotate tool is inactive

2. ..and of course you are on the rotate tool.

Clicking on the canvas brings up the rotate dialogue.

3. Various ways to rotate. Enter a value manually, use the slider or click and drag in the canvas. Note the layer visibility temporarily goes off. That is normal.

4. This is where it gets a bit strange from your description. Clicking on Rotate button or Hit the Enter key to apply. The Dialogue should close. If the Rotate button is greyed out or you need to close the dialogue then my advice is: Choose another tool, back to the rotate tool, start again.

5. Just a note about layer size after rotation. This depends on the Clipping setting in the tool options.

6. Why does the Rotate tool reappear? You are still using the Rotate Tool. Gimp is not a mind-reader. Change to another tool.