feat: Add Beads MCP Server [bd-5]

Implements MCP server for beads issue tracker, exposing all bd CLI functionality to MCP clients like Claude Desktop.

Features:
- Complete bd command coverage (init, create, list, ready, show, update, close, dep, blocked, stats)
- Type-safe Pydantic models with validation
- Comprehensive test suite (unit + integration tests)
- Production-ready Python package structure
- Environment variable configuration support
- Quickstart resource (beads://quickstart)

Ready for PyPI publication after real-world testing.

Co-authored-by: ghoseb <baishampayan.ghose@gmail.com>

integrations/beads-mcp/README.md

@@ -0,0 +1,91 @@
+# beads-mcp
+
+MCP server for [beads](https://github.com/steveyegge/beads) issue tracker and agentic memory system.
+Enables AI agents to manage tasks using bd CLI through Model Context Protocol.
+
+## Installing
+
+```bash
+git clone https://github.com/steveyegge/beads
+cd beads/integrations/beads-mcp
+uv sync
+```
+
+Add to your Claude Desktop config:
+
+```json
+{
+  "mcpServers": {
+    "beads": {
+      "command": "uv",
+      "args": [
+        "--directory",
+        "/path/to/beads-mcp",
+        "run",
+        "beads-mcp"
+      ],
+      "env": {
+        "BEADS_PATH": "/home/user/.local/bin/bd",
+      }
+    }
+  }
+}
+```
+
+**Environment Variables** (all optional):
+- `BEADS_PATH` - Path to bd executable (default: `~/.local/bin/bd`)
+- `BEADS_DB` - Path to beads database file (default: auto-discover from cwd)
+- `BEADS_ACTOR` - Actor name for audit trail (default: `$USER`)
+- `BEADS_NO_AUTO_FLUSH` - Disable automatic JSONL sync (default: `false`)
+- `BEADS_NO_AUTO_IMPORT` - Disable automatic JSONL import (default: `false`)
+
+## Features
+
+**Resource:**
+- `beads://quickstart` - Quickstart guide for using beads
+
+**Tools:**
+- `init` - Initialize bd in current directory
+- `create` - Create new issue (bug, feature, task, epic, chore)
+- `list` - List issues with filters (status, priority, type, assignee)
+- `ready` - Find tasks with no blockers ready to work on
+- `show` - Show detailed issue info including dependencies
+- `update` - Update issue (status, priority, design, notes, etc)
+- `close` - Close completed issue
+- `dep` - Add dependency (blocks, related, parent-child, discovered-from)
+- `blocked` - Get blocked issues
+- `stats` - Get project statistics
+
+
+## Development
+
+Run MCP inspector:
+```bash
+# inside beads-mcp dir
+uv run fastmcp dev src/beads_mcp/server.py
+```
+
+Type checking:
+```bash
+uv run mypy src/beads_mcp
+```
+
+Linting and formatting:
+```bash
+uv run ruff check src/beads_mcp
+uv run ruff format src/beads_mcp
+```
+
+## Testing
+
+Run all tests:
+```bash
+uv run pytest
+```
+
+With coverage:
+```bash
+uv run pytest --cov=beads_mcp tests/
+```
+
+Test suite includes both mocked unit tests and integration tests with real `bd` CLI.