I believe I'm having the same problem. I've created a Newsletter block, with a Google Sheet as the storage option. Squarespace sends the information to the Google Sheet correctly, but Google doesn't send the notification email to me. I suspect it's because Google thinks I'm making the edit, rather than Squarespace, so it doesn't send the email.
I tried to get around this by creating a new Google account just for this purpose, but the same thing happens.
https://support.google.com/docs/answer/91588?co=GENIE.Platform%3DDesktop&hl=en
Does anyone have any suggestions?