Bimmer forums to the rescue! https://www.bimmerforums.co.uk/threads/e46-touring-how-to-repair-rear-washer.25412/
Yep that’s about it, I had the same issue (E61).
@Nef started
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Bimmer forums to the rescue!
https://www.bimmerforums.co.uk/threads/e46-touring-how-to-repair-rear-washer.25412/