feat: run docs-mcp as a long-lived shared HTTP service

context-docs was previously spawned per call as a fresh stdio container,
which meant every MCP request paid full cold-start cost (embedding model
load + Chroma open) and concurrent clients raced for the same Chroma
writer. The 50+ orphan container build-up I saw during the publish audit
was the visible symptom.

This refactor runs docs-mcp as one long-lived service:

- compose: docs-mcp leaves the 'mcp' profile, gets container_name,
  restart: unless-stopped, healthcheck, and a host port (127.0.0.1:8776
  by default). Runs as the host UID/GID so bind mounts don't end up
  root-owned.
- docker image: adds mcp-proxy (0.12.0) and an entrypoint that fronts
  llms-txt-mcp's stdio as Streamable HTTP. Reads sources from a flat
  file mounted at /etc/context-kit/docs-sources.txt. Disables eager
  preindex by default; callers refresh on demand via the docs_refresh
  tool. Set CONTEXT_KIT_DOCS_PREINDEX=1 to restore eager behavior.
- bin/context-kit: 'start' brings up the docs service alongside SearXNG,
  generates the sources file from CONTEXT_KIT_DOCS_SOURCES, and waits
  for the HTTP endpoint to become ready (up to 180s for first-run model
  download). 'docs' still works for stdio-only clients but is now a
  thin mcp-proxy bridge onto the shared HTTP service. 'doctor' and
  'status' both surface the new endpoint.
- install snippets: context-docs is now 'type: remote'/'type: http'
  pointing at ${CONTEXT_KIT_DOCS_HTTP_URL}. HTTP-capable MCP clients
  bypass the bridge entirely. snippets/*.json and the install command
  output stay byte-identical.
- docs and .env.example updated for new vars (CONTEXT_KIT_DOCS_PORT,
  CONTEXT_KIT_DOCS_HTTP_URL, CONTEXT_KIT_DOCS_PREINDEX) and the new
  24h TTL default (down from 7d; the long-lived service makes shorter
  defaults cheap).

Verified end-to-end:
- compose config -q, bash -n, sh -n all clean
- HTTP /status returns 200
- stdio bridge returns initialize + tools/list with the same 3 tools
  (docs_sources, docs_refresh, docs_query)
- doctor passes all 10 checks including the new HTTP probe
- web-search and repomix MCP handshakes still work
- redaction-check clean
- install JSON valid for both targets + --absolute

README.md

@@ -56,8 +56,12 @@ config that will not be committed.
 ## Defaults
 
 - SearXNG binds to `127.0.0.1:8099` only.
+- `context-docs` runs as a long-lived service on `127.0.0.1:8776` (Streamable
+  HTTP MCP) so every client shares one indexer and one Chroma writer. The
+  `bin/context-kit docs` stdio command is kept as a compatibility shim for
+  clients that cannot speak HTTP MCP.
 - Docs and model caches live in `$HOME/.local/share/context-kit`.
-- Docs refresh TTL defaults to `7d`.
+- Docs refresh TTL defaults to `24h`.
 - MCP containers are labeled `dev.context-kit=true` for safe inspection and cleanup.
 - Repomix mounts only the current project read-only, not your whole home directory.
 - No code-editing MCP server is enabled by default.