Implement daemon auto-start with comprehensive improvements (bd-124)

- Auto-starts daemon on first bd command (unless --no-daemon or BEADS_AUTO_START_DAEMON=false)
- Exponential backoff on failures: 5s, 10s, 20s, 40s, 80s, 120s (max)
- Lockfile prevents race conditions when multiple commands start daemon simultaneously
- Stdio redirected to /dev/null to prevent daemon output in foreground
- Uses os.Executable() for security (prevents PATH hijacking)
- Socket readiness verified with actual connection test
- Accepts multiple falsy values: false, 0, no, off (case-insensitive)
- Working directory set to database directory for local daemon context
- Comprehensive test coverage including backoff math and concurrent starts

Fixes:
- Closes bd-1 (won't fix - compaction keeps DBs small)
- Closes bd-124 (daemon auto-start implemented)

Documentation updated in README.md and AGENTS.md

Amp-Thread-ID: https://ampcode.com/threads/T-b10fe866-ab85-417f-9c4c-5d1f044c5796
Co-authored-by: Amp <amp@ampcode.com>

AGENTS.md

@@ -53,6 +53,8 @@ bd daemon --global
 # MCP server automatically discovers and uses the global daemon
 ```
 
+**Note:** As of v0.9.11, the daemon **auto-starts automatically** when you run any `bd` command. You typically don't need to manually start it. To disable auto-start, set `BEADS_AUTO_START_DAEMON=false`.
+
 Your MCP config stays simple:
 ```json
 {
@@ -67,6 +69,7 @@ The MCP server will:
 1. Check for local daemon socket (`.beads/bd.sock`)
 2. Fall back to global daemon socket (`~/.beads/bd.sock`)
 3. Automatically route requests to the correct database based on your current working directory
+4. Auto-start the daemon if it's not running (with exponential backoff on failures)
 
 **Option 2: Multiple MCP Server Instances**
 Configure separate MCP servers for each major project: