fix(link-checker): distinguish empty diffs from unavailable bases

[BichengWang]

--changed falls through to older refs when a successful diff contains no changed Markdown or notebooks. A branch identical to origin/main can consequently audit unrelated notebooks. When every comparison base is unavailable, the fallback also reports no modified files and exits without scanning the repository.

Stop at the first successful diff, including empty and Python-only diffs. Return None when no base is available so the CLI performs the promised full audit. Add selection and CLI regressions, including a fresh Git repository without commits.

Validation:

• python3 -m unittest tools/test_check_all_links.py -v: 15 tests pass on Python 3.11. The two unavailable-base regressions fail before the fallback fix.
• Actual --changed CLI, Pyink on changed lines, Python compilation, and git diff --check pass.

[gemini-code-assist]

Summary of Changes

Hello, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request improves the reliability of the link checker's --changed flag. Previously, the tool would incorrectly fall back to older commits if a diff contained no changes to documentation files, potentially triggering audits on unrelated broken links. The changes ensure that a successful diff—even if empty or containing only non-documentation files—is respected as the comparison base, while maintaining appropriate fallback behavior for unavailable references.

Highlights

• Link Checker Logic: Updated the link checker to correctly handle empty diffs when selecting a base, preventing it from falling back to older refs when no relevant Markdown or notebook files have changed.
• Regression Testing: Added comprehensive unit tests to verify that the tool stops at the first successful diff and correctly handles fallback scenarios when upstream refs are unavailable.

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[gemini-code-assist]

Code Review

This pull request updates tools/check_all_links.py to return the list of changed files once a successful comparison base is established, even if the list is empty, and adds comprehensive unit tests in tools/test_check_all_links.py. Feedback on the changes points out that the fallback logic is broken when no base branch can be determined, as returning a falsy value causes the script to exit early instead of falling back to scanning all files. A code suggestion is provided to properly handle this fallback behavior.