gh-stack is impossible to install: API rate limit exceeded

```
% gh extension install github/gh-stack
could not check for binary extension: HTTP 403: API rate limit exceeded for A.B.C.D. (But here's the good news: Authenticated requests get a higher rate limit. Check out the documentation for more details.) (https://api.github.com/repos/github/gh-stack/releases/latest)
```

Start by reproducing `gh extension install github/gh-stack` and inspect the installation path that requests `https://api.github.com/repos/github/gh-stack/releases/latest`. Confirm the failure mode with an unauthenticated request and define the expected behavior; done means the extension can be installed without this rate-limit failure.

Written by the indexing model from the issue text.