Hi Lesley. Thanks very much for responding to my question.
That's what I would have expected. But when I asked Squarespace about this, they told me "our system is designed to make sure that Google does not penalise for multiple H1 tags." and "When Google indexes and ranks your site, it will take your first H1 tag as being your site title and it will not take the other H1 tags into account negatively.".
I'm far from being an expert - hence asking on here to get some expert opinion. But to me, Squarespace's answer contradicts the accepted approach for good practice. I'm currently looking at trying to rectify this somehow, but I suspect the structure is 'hard-wired' into Squarespace.
Again, thanks for taking the time to answer Lesley. Much appreciated.