feat(skill): add LiteLLM AI gateway operations skill

Add litellm/, an operational tool skill for the LiteLLM AI gateway (proxy)
and Python SDK, in the same vein as the vllm and llama-cpp engine skills.

Contents:
- SKILL.md: operating contract, operating loop, verification boundaries,
  and hard boundaries; concise core sections routing depth to references
- README.md: human-facing install/use guide with required sections
- references/: nine dated, source-indexed references (source index,
  quickstart + SDK, config & routing, keys/teams/budgets/spend, caching &
  guardrails, observability & logging, deployment, security & public
  hosting, troubleshooting), researched against litellm 1.97.0
  (2026-08-22) including a live proxy probe of the health endpoints
- scripts/litellm-health: read-only GET-only probe (liveliness, readiness,
  /v1/models, /model/info); stdlib-only Python 3.9+, --json, --help
  without a server
- tests/test_litellm_health.py: 18 deterministic tests against a local
  stub HTTP server, including the observed-traffic GET-only contract
- templates/proxy-config-record.md and proxy-deployment.md: fillable
  records; the config record is the rollback unit
- evals/evals.json: schema_version 1, six output-quality cases

Also regenerates tracked catalog artifacts (.claude-plugin/marketplace.json,
.codex-plugin/plugin.json, llms.txt) and adds the root README catalog entry
plus the skill-triggers.md index row.

AI assistance: authored with AI assistance (Factory Droid) under human
direction; facts verified against litellm 1.97.0 and official docs dated
2026-08-22.

Co-authored-by: factory-droid[bot] <138933559+factory-droid[bot]@users.noreply.github.com>

.codex-plugin/plugin.json

@@ -90,6 +90,7 @@
     "./legal-strategy",
     "./life-coach",
     "./linear",
+    "./litellm",
     "./llama-cpp",
     "./llamaindex",
     "./mermaid-diagrams",