Adapt language ecosystem native API docs practices wherever possible

Work items in this epic deal with bringing all supported languages to parity with Java regarding support for the expected practices for API docs in that language ecosystem.

For Java, we already have:

- https://javadoc.io/doc/com.github/copilot-sdk-java/latest/index.html
- https://github.github.com/copilot-sdk-java/1.0.1/apidocs/com.github.copilot.java/module-summary.html

## API Docs Ecosystem Summary

| Ecosystem | Doc artifact required to publish? | Auto-hosted docs site | Culture strength |
|-----------|----------------------------------|----------------------|-----------------|
| **Java** | ✅ Yes (Maven Central mandate) | javadoc.io (3rd party) | Strong |
| **Node/TS** | ❌ No | tsdocs.dev (3rd party, unreliable — see note below) | Moderate |
| **Python** | ❌ No | Read the Docs (opt-in) | Strong convention |
| **Go** | ❌ No (but comments are the format) | pkg.go.dev (1st party, automatic) | Very strong |
| **.NET** | ❌ No (but XML doc conventionally included) | fuget.org (3rd party) | Strong |
| **Rust** | ❌ No (but comments are the format) | docs.rs (1st party, automatic) | Very strong |

> **Note on tsdocs.dev:** As of 2026-06-13, tsdocs.dev returns 502 Bad Gateway across all URLs. It is a volunteer-run third-party project with no backing from npm or Microsoft and no SLA. It should not be relied upon as a primary docs hosting solution for `@github/copilot-sdk`. Self-hosted TypeDoc output (e.g. GitHub Pages from CI) is the only reliable option for TypeScript.

**Bottom line:** Go and Rust have the closest parity to Java's "publish once, docs appear everywhere" model — but achieved through first-party infrastructure rather than a mandated artifact. Python and .NET have strong doc cultures but require explicit hosting setup. TypeScript is the weakest — tsdocs.dev is unreliable (currently down), so self-hosted docs are a necessity.