Ok - I got to the bottom of it 
With the “Develop” menu visible (set “Show features for web developers” in the Settings Advanced tab) there are a number of feature flags available. There’s a whole bunch of disabled CSS features identified as either “Preview” or “Testable”. One of the latter category is “CSS Unprefixed Backdrop Filter”. If I turn this on, background blurs render correctly.
It sounds as though this feature is now turned on by default in the recently released Safari 26. However, there will be a lot of earlier versions out there for a while, so beware when using background blurs that some users might not get to appreciate some of the subtleties of your page design!