Hello Joris,
You may want to try the Lung CT Segmenter module of the Lung CT Analyzer extension which includes an option for airway segmentation.
I manually annotated one of the segmentations like this:
There is no computerized bronchopulmonary segment annotation available in Slicer yet - it would probably be interesting to train AI on a set of segmentations to do this automatically or use the VMTK for centerline calculations.