docs: publish Sourcey C API reference

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Summary

• generate a searchable C API reference from libamtrack's public headers with Sourcey 3.6.5 and Doxygen XML
• publish the generated reference at the project-owned /api/ route through the existing GitHub Pages workflow
• pin the library input to commit ef78da9ac3342dadbc1854df9534d45ccaeeb3c9
• add a navigation link from the Docusaurus site to the C API reference

Implementation

• checks out the pinned libamtrack/library source during deployment
• prepares temporary Doxygen groups without modifying the library repository
• generates Doxygen XML and builds the Sourcey reference into static/api
• rewrites generated page links for the /api/ base path and removes unresolved local links
• keeps generated inputs and output out of version control

Validation

The complete pipeline was run locally against the pinned source revision:

• Docusaurus production build: passed
• generated pages: 68
• documented functions: 446
• indexed symbols: 514
• search entries: 1,619
• source links pinned to the library revision: 195
• unresolved generated links: 0
• local path or secret leakage detected: 0

Related to libamtrack/library#294.

AI disclosure

AI assisted with the documentation pipeline and drafting. The generated output, navigation, symbol coverage, links, and pinned source revision were manually checked before submission.