Hello, my customers are having the same issue! Was this ever resolved anywhere where I could see the solution? Thank you! Really hoping to fix this!
UPDATE:
I believe I found a solution that may be helpful! On my site, my shipping options were all calculated. However, I am not paying for the version of Squarespace that allows calculated shipping rates. Hence, none of them showed up at checkout, and my customers could not continue past shipping (because they could not choose a delivery option.) I went into Shipping settings, changed all my rates to a flat rate, and added the prices manually, and they all showed up at checkout.
Now the continue button is visible, and my customers can move on to the next step in the checkout process.
I hope this helps anyone who has the same problem!