resizing a QTreeWidget

[wysota]

...by knowing how many item one wants to show and how much space each
of them will use up and how much space there is available, I presume.

I don't know is such assumptions are appropriate. Calling verticalScrollBar()->isVisible() might be more reliable.

Qt doesn't seem to know [whether a scrollbar is needed] by the time sizeHint is called;

That doesn't matter. You can change the size hint once the widget is rendered for the first time using QWidget::updateGeometry().

The scrollbar width() always returns 100 there, it changes into 16 once it is actually rendered on screen.

Yes, that's normal for every widget.