Surprised nobody mentioned the extremely annoying and misleading 404 response when you are denied permission to view a private repo. I can't tell you how many times people at work tell me my link doesn't work because they aren't signed-in.
All we need is an error code 402.5 "plausible deniability between unauthorized and not found"...
For the rest of your users it wouldn't hurt to say, "You might see something different if you're logged in." Or if they are logged in, saying, "Were you expecting something different? Maybe you just don't have access yet."