As Squarespace has a partnership with Google, I'm hoping that one day soon they'll introduce a Product Reviews feature that shows Google Reviews.
Sadly, there isn't a free solution right now that shows Google Reviews. If you want to automatically display Google Reviews on your site, you can only do so by paying for one of the third-party solutions that connect to Google's API.
If you would be happy using an alternative review service, YotPo offer a free tier.
Thank you for your answer. Yes it seems odd to have to pay yet another service to do something so simple given how interoperable squarespace and google seem to be.