CI: Check that API documentation builds without warnings

[alexdewar]

I just noticed that cargo doc is emitting a warning for our code, but I didn't noticed until now, because, while we do build and the API documentation on pushes to main, at no point do we check for warnings.

This PR adds a workflow to do this for PRs. The docs workflow is also changed to fail on warnings; while this means that docs with warnings won't be published, it also means we'll get an email if we break the documentation on main.

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 79.89%. Comparing base (5f54705) to head (5cc62f0). Report is 2 commits behind head on main.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #126 +/- ## ======================================= Coverage 79.89% 79.89% ======================================= Files 9 9 Lines 199 199 ======================================= Hits 159 159 Misses 40 40 ```

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