There is an integration called Feedbolt for WordPress that does this automatically, but I doubt there is anything for SquareSpace. You could just send out an email broadcast manually to your list when you post a new blog post.
To get a web form on a SquareSpace personal page, you’ll have to edit the web form code to remove some scripts as SquareSpace does not allow <script>
tags on the personal plan.
- Create a campaign that starts with a web form that leads to a sequence. The sequence adds a “newsletter” tag (or whatever you want to name it.)

- Grab the web form code (unstyled HTML)

- Remove all the scripts at the bottom. but beware, this will open you up to bot spamming as you aren’t going to be able to use Google ReCAPTCHA.

-
Put the rest of the code into a code block on your page and you are good to go.
-
Now, when you post your blog, just send out an email broadcast to those you tagged “Newsletter” in your campaign.