docs: verify extension.rst against the current server implementation and rewrite reference/extension

[coretl]

Target page

reference/extension

The page is a full stub — the source (extension.rst) is flagged as outdated
and needs verification against the current implementation before it can be
converted.

Category: verify-then-write

What a human must do (~3–4 hours)

1. Read docs/_legacy_rst/extension.rst (739 words: Extension Modules,
   Injected Values).
2. Compare against the current server source code for the extension server
   (socket protocol, injected value names, lifecycle hooks).
3. Identify:
   • What has changed since the doc was written.
   • What is still accurate and can be kept.
   • What is missing (new injected values, new API calls).
4. Write the updated reference/extension.md with verified content.

Post as a PR against the docs branch.

Source

docs/_legacy_rst/extension.rst — 739 words (Extension Modules, Injected
Values).