Groups: add user to all projects at once?

Sorry if this is a FAQ, or if there’s documentation on it, I couldn’t find anything, so I’m asking here.

I have a lot of people who work on a number of projects. I’ll want to add projects over time, and people will come and go. What I want is:

  1. when I add a new project, I want everyone in the group to have Guest access to it by default.

  2. when I add a new user to a group, I want them to have Guest access to all the projects by default.

  3. when a user leaves our institute, I want to be able to remove them from all projects in one go, by removing them from the group.

So, I want to avoid having to manage N users x M projects one by one, which doesn’t scale well as either N or M grows. In my case, both N and M are on the order of 100-200.

My mental model for how groups ought to work is that I add people to groups, and groups to projects, which gives me most of what I want. Is that how it works?

Thanks in advance for any help.