docs(mcp): switch MCP transport stdio → SSE, update all references

MCP server is now a persistent SSE service on :8001 (make mcp-http),
independent of the Claude Code session. Re-registration is a single
claude mcp add-json command; no patch_mcp_cwd.py needed.

- Makefile: mcp-http is primary transport, add fuser restart + updated comment
- state-hub/README.md: stack table, MCP section, troubleshooting note updated
- CLAUDE.md (project): registration instructions rewritten for SSE

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

CLAUDE.md

@@ -64,7 +64,7 @@ make dashboard                # Observable preview on :3000
 make check                    # curl /state/health
 ```
 
-The MCP server is registered in `.mcp.json` at the repo root. After `make install` creates `.venv`, restart Claude Code for `/mcp` to show `state-hub`.
+The MCP server runs as a persistent SSE service (`make mcp-http`, port 8001). Registered at user scope via `claude mcp add-json -s user state-hub '{"type":"sse","url":"http://127.0.0.1:8001/sse"}'`. Restart the MCP server independently — no Claude Code restart needed.
 
 ### Docker Setup (WSL2, one-time)