docs: sync HINDSIGHT_API_LLM_PROVIDER lists with canonical configuration table

[r266-tech]

Summary

Sync the HINDSIGHT_API_LLM_PROVIDER list across three top-level surfaces with the canonical configuration table at hindsight-docs/docs/developer/configuration.md.

The recent opencode-go addition in #1652 (and earlier providers like claude-code, openai-codex, vertexai, bedrock, litellm, litellmrouter, volcano, openrouter, deepseek, zai, llamacpp) had been fully wired into hindsight_api/config.py, llmProviders.json, configuration.md, and models.mdx — but three surfaces still carried the legacy 6–7 provider shortlist.

Drift

• README.md (last meaningful provider update: 2026-03-13, feat: add MiniMax LLM provider support #550 MiniMax) — sentence claims "Valid options are ...", which read as a complete list. Missing 13 providers.
• hindsight-api/README.md (last update: 2026-01-01, feat(doc): add new config options and supported providers #84) — config env-var table row missing 14 providers.
• CLAUDE.md (provider line predates current set) — bullet missing 13 providers.

hindsight-docs/versioned_docs/version-0.6/... intentionally left untouched (Docusaurus snapshot pattern, frozen to that release).

Change

For each file, the provider list is brought into alignment with the canonical configuration table:

openai, openai-codex, claude-code, anthropic, gemini, groq, minimax, deepseek, zai, opencode-go, ollama, lmstudio, llamacpp, vertexai, bedrock, litellm, litellmrouter, volcano, openrouter, none

Format preserved per-file (inline backtick list in README.md, table cell in hindsight-api/README.md, plain bullet in CLAUDE.md).

Notes

• No code, defaults, or tests touched.
• No auto-generation script targets these three files (scripts/generate-docs-skill.sh regenerates the skills/hindsight-docs mirror only).
• Each provider is present in hindsight-docs/src/data/llmProviders.json, so the data layer already knew the full set.

Happy to drop a particular surface if it was intentionally curated short.