How do I stop / pause / hide / or un-publish a project I'm working on without deleting it? It seems the only two option are active or deleted. I still want to keep the project, logs and everything else, I just don't want anyone accessing it. How do I continue to work on a project (privately) without having people access it after sharing it for test purposes?

I don't know if there is a feature request for pausing/archiving a project, but I can check for you.

Any further help on this? From my standpoint it looks like Vapi thinks "every project" should be active, live, running. Not even a single option to "archive" or "pause" a project.? Only discard and delete options?

You can create a new organization and keep your project over there. This way, the members of your org can only access it. But if you're saying "don't even want Vapi team to find it," that's not technically possible.