The available options depend on the kind of the shape. They can be better seen in
Text than in the Position and Size dialog. The “Fit width to text” and “Fit height to text” settings belong to a text-box. Therefore they are disabled in the Position and Size dialog, if the object is not a text-box.
The UI, the current behavior, and the file format does not fit well together. So you need to test, which kind of shape gives the desired behavior. To get a “rectangle” you can use: A legacy rectangle, a path, a polygon, a custom shape or a text box.
You can try these:
A custom shape with “Word wrap text in shape” on and “Resize shape to fit text” on. The width is kept as you have set it, and height will grow/shrink, when you enter more text or remove text.
A text-box (you can set line and filling as for other shapes) with “Fit width to text” on and “Fit height to text” on. But it has no auto scale in all cases. After removing lines, you need to drag the bottom edges yourself. And the width is bound to the paragraph width, no wrap available.