I looked at your staging site, and checked the template for displaying posts, as well as one of the posts themselves (8 documentaries...).
First, let me say that the last update of Blocks fixed some issues with auto-paragraphs, and when I just tested it on my own site it appears to be working correctly. You have used a Fields and Text block to output your post-body custom field, wrapped in wpv-autop tags, but I suggest you simply use the Single Field block in place of the Fields and Text block, and no special handling is required.
I tried that on your staging site, but I could see on the backend preview it wasn't working (I didn't save the changes to the template).
But when I edited the post I could see why.
In the screenshot, note the section of text I'm inspecting.
On your production site there are line breaks within that text, but on the staging site it is continuous.
But when I edited the post I could see that the post-body WYSIWYG field is in HTML mode (rather than Visual), and the relevant text is as follows:
<p>Does this sound familiar? Here's a suggestion for you! Why not check out these documentaries related to art and social change! These documentaries raise some very important questions and, perhaps, will spark some new ideas, thoughts and discussion. Note: This list is in no particular order or preference. <strong>Searching for Sugar man (2012)</strong></p>
Note how it is all within one set of p tags, hence it is to be expected that the text displays as a single paragraph, nothing broken with the template.
I assume that on the production site if you edit the same post you will find it is different (otherwise where could the line breaks you see come from?).
I don't know why it's different, but that must be the explanation.