Embedding to Squarespace is different from a standard embed. Here's how to embed your Paperform forms on Squarespace:
Some Squarespace themes have "Ajax" loading enabled. This is a feature that some Squarespace themes have enabled by default, which loads page navigations using javascript.
This makes the pages load faster, but the downside is that any javascript that is on the new page isn't fired. This means your Paperform forms can behave unexpectedly while embedded.
There are two workarounds for this:
<script src="https://paperform.co/__embed"></script>