Implement BEADS_DIR environment variable (bd-e16b)

Add BEADS_DIR as a replacement for BEADS_DB to point to the .beads
directory instead of the database file directly.

Rationale:
- With --no-db mode, there's no .db file to point to
- The .beads directory is the logical unit (contains config.yaml, db
  files, jsonl files)
- More intuitive: point to the beads directory not the database file

Implementation:
- Add BEADS_DIR environment variable support to FindDatabasePath()
- Priority order: BEADS_DIR > BEADS_DB > auto-discovery
- Maintain backward compatibility with BEADS_DB (now deprecated)
- Update --no-db mode to respect BEADS_DIR
- Update MCP integration (config.py, bd_client.py)
- Update documentation to show BEADS_DIR as preferred method

Testing:
- Backward compatibility: BEADS_DB still works
- BEADS_DIR works with regular database mode
- BEADS_DIR works with --no-db mode
- Priority: BEADS_DIR takes precedence over BEADS_DB

Follow-up issues for refactoring:
- bd-efe8: Refactor path canonicalization into helper function
- bd-c362: Extract database search logic into helper function

Closes bd-e16b

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

beads.go

@@ -118,12 +118,61 @@ func NewSQLiteStorage(dbPath string) (Storage, error) {
 }
 
 // FindDatabasePath discovers the bd database path using bd's standard search order:
-//  1. $BEADS_DB environment variable
-//  2. .beads/*.db in current directory or ancestors
+//  1. $BEADS_DIR environment variable (points to .beads directory)
+//  2. $BEADS_DB environment variable (points directly to database file, deprecated)
+//  3. .beads/*.db in current directory or ancestors
 //
 // Returns empty string if no database is found.
 func FindDatabasePath() string {
-	// 1. Check environment variable
+	// 1. Check BEADS_DIR environment variable (preferred)
+	if beadsDir := os.Getenv("BEADS_DIR"); beadsDir != "" {
+		// Canonicalize the path to prevent nested .beads directories
+		var absBeadsDir string
+		if absPath, err := filepath.Abs(beadsDir); err == nil {
+			if canonical, err := filepath.EvalSymlinks(absPath); err == nil {
+				absBeadsDir = canonical
+			} else {
+				absBeadsDir = absPath
+			}
+		} else {
+			absBeadsDir = beadsDir
+		}
+
+		// Check for config.json first (single source of truth)
+		if cfg, err := configfile.Load(absBeadsDir); err == nil && cfg != nil {
+			dbPath := cfg.DatabasePath(absBeadsDir)
+			if _, err := os.Stat(dbPath); err == nil {
+				return dbPath
+			}
+		}
+
+		// Fall back to canonical beads.db for backward compatibility
+		canonicalDB := filepath.Join(absBeadsDir, CanonicalDatabaseName)
+		if _, err := os.Stat(canonicalDB); err == nil {
+			return canonicalDB
+		}
+
+		// Look for any .db file in the beads directory
+		matches, err := filepath.Glob(filepath.Join(absBeadsDir, "*.db"))
+		if err == nil && len(matches) > 0 {
+			// Filter out backup files and vc.db
+			var validDBs []string
+			for _, match := range matches {
+				baseName := filepath.Base(match)
+				if !strings.Contains(baseName, ".backup") && baseName != "vc.db" {
+					validDBs = append(validDBs, match)
+				}
+			}
+			if len(validDBs) > 0 {
+				return validDBs[0]
+			}
+		}
+
+		// BEADS_DIR is set but no database found - this is OK for --no-db mode
+		// Return empty string and let the caller handle it
+	}
+
+	// 2. Check BEADS_DB environment variable (deprecated but still supported)
 	if envDB := os.Getenv("BEADS_DB"); envDB != "" {
 		// Canonicalize the path to prevent nested .beads directories
 		if absDB, err := filepath.Abs(envDB); err == nil {
@@ -135,7 +184,7 @@ func FindDatabasePath() string {
 		return envDB // Fallback to original if Abs fails
 	}
 
-	// 2. Search for .beads/*.db in current directory and ancestors
+	// 3. Search for .beads/*.db in current directory and ancestors
 	if foundDB := findDatabaseInTree(); foundDB != "" {
 		// Canonicalize found path
 		if absDB, err := filepath.Abs(foundDB); err == nil {