Can't they still track you by IP address? (assuming you have a unique address)
Piggybacking on this (as I do it too) how robust is this method?
You've just given them permission to fingerprint you. If they're good at what they do then the private window trick had no effect.
Moderately. From a few years ago, I remember Yahoo was still able to triangulate pretty well on whichever device you were using, but had more difficulty across devices. Deduplication was a bit of an art at that point.