How to show a block between the body and a paragraphs field?
Enable "Layout builder" module first. On "Manage display" in entity config Default "Custom display" enable "Full content", then go there and enable "Use Layout builder" and "Allow each content item to have its layout customized."

This will give you "Layout" tab in each node (of this type where you enable this in config) for ex. - how to arrange each field of this entity, also ability to add custom block, user fields, etc. If you want Contact form there you should probably have to write custom block in custom module and put the form inside - just to have it for placement from the Layout builder.