I made that division, because I think the project consists of 3 separate parts, that can be implemented more or less independently of each other.
Re: Public judgment. Yes, your description is accurate. It is the way in which the public is able to review the practices of a business without the help or even knowledge of the business itself. Judging from the outside. The reviews thus collected would serve other potential users / customers to inform themselves. Very similar to what you see in e.g. the Appstore or Google Play, but more specific than just a 4-star rating.
The checklist for the public tries to provide insights on: “Does the company have a privacy policy?”, “Is the privacy policy clear and easy to understand?”, “Does the company provide my PII to 3rd-parties?”, “Does the website contain trackers?”, “Does the App contain trackers?”, “Is the revenue model of the company clear?”
The company can also answer these questions themselves, so the questions are part of “Declared principles”, but these then go further with e.g. ethics compliance, fair work scores, diversity policy, etc.
Based on “public judgment” we could already design a label / logo that has e.g. a color ranging from red to green, and a score shown within. But this would not provide certification.
Humane Tech Certification, as you say, would be very challenging to set up. I think here - on the short term - the community can only provide guidance for others to set this up. There is a niche here where consultants and new businesses can jump in to provide this. On the longer term the HTC can be the authoritative source of “Declared principles” and “Auditing the auditors” e.g. provide a directory of trusted auditors and consultants.
But this whole project starts with collecting information for the checklists. I created a Wiki post for brainstorming: