Ideally, you should have a proper UTM strategy in place to capture the source of an interaction  (i.e., sign up form fills) accurately instead of relying on the referrer data. AFAIK, the current referrer policy reveals only the referrer data with only domain URLs w/o parameters, url path, etc. (if someone lands to your page from example.com/abc123?q=a, document.referrer would only show referrer as https://www.example.com or no referrer data at all) for the cross site navigation. For the same site navigation, you should be good to retain the referrer data IMO. Also, to be clear, Within the context of a Filled Out Form activity, the Referrer constraint is the page the form was on. It is not the page prior to that page. The document.referrer works on the Visited Web Page activity.

Check out Sandy’s post regarding the referrer policy: 

Here’s why your “Autofill from Referrer Parameter” setup stopped working