CI: Check broken links in src doc comments

### Is your feature request related to a problem or challenge?

https://github.com/apache/datafusion/pull/16830 fixed several invalid links in the doc comments.

It would be great to setup a CI job, to check those links automatically.

### Describe the solution you'd like

`cargo-deadlinks` can be helpful https://github.com/deadlinks/cargo-deadlinks

### Describe alternatives you've considered

_No response_

### Additional context

_No response_

The issue names no CI file or test; start by locating the repository's CI configuration and reviewing the linked cargo-deadlinks project. Define how the check should cover Rust doc comments under src, and consider the work done when CI reliably reports broken links without disrupting unrelated checks.

Written by the indexing model from the issue text.