Who should I tell about switching a group-based course to pass/no credit?
First of all, saving this group project should be your top-priority. This is still in your personal interest since failing projects tend to get people failed in the class entirely. Also: later in life you are going to have to work with other people and things might get very difficult. Turning this around now is valuable experience for later in life when there is really something at stake.
My advice would be to talk to your group members and make a plan to get things going. If the problem is other group members refusing to work or handing in significantly sub-standard work, talk to your professor about it now. 4 Weeks is enough time to get a lot done, that gets a lot harder with 3 or even 2 weeks left.
The issue isn't that you might appear to abandon them. You yourself are now planning to put less work into it than what you yourself think the project needs to succeed. So the problem is that to a degree you are abandoning the project.