Implement exclusive lock protocol for daemon/external tool coexistence

- Add ExclusiveLock struct with JSON marshaling and validation
- Implement IsProcessAlive() with EPERM fail-safe behavior
- Add ShouldSkipDatabase() with stale lock cleanup
- Integrate lock checking into daemon sync cycle
- Return holder name on stale removal for better logging
- Case-insensitive hostname comparison
- Comprehensive unit tests (89.3% coverage)
- Documentation updates (ADVANCED.md, AGENTS.md)
- Add .beads/.exclusive-lock to .gitignore

Closes bd-115, bd-116, bd-117, bd-118, bd-119, bd-120, bd-121, bd-122

Amp-Thread-ID: https://ampcode.com/threads/T-0b835739-0d79-4ef9-aa62-8446a368c42d
Co-authored-by: Amp <amp@ampcode.com>

cmd/bd/daemon.go

@@ -927,6 +927,21 @@ func createSyncFunc(ctx context.Context, store storage.Storage, autoCommit, auto
 			return
 		}
 
+		// Check for exclusive lock before processing database
+		beadsDir := filepath.Dir(jsonlPath)
+		skip, holder, err := types.ShouldSkipDatabase(beadsDir)
+		if skip {
+			if err != nil {
+				log.log("Skipping database (lock check failed: %v)", err)
+			} else {
+				log.log("Skipping database (locked by %s)", holder)
+			}
+			return
+		}
+		if holder != "" {
+			log.log("Removed stale lock (%s), proceeding with sync", holder)
+		}
+
 		if err := exportToJSONLWithStore(syncCtx, store, jsonlPath); err != nil {
 			log.log("Export failed: %v", err)
 			return