Add daemon health check endpoint (bd-146)

- Add OpHealth RPC operation to protocol
- Implement handleHealth() with DB ping and 1s timeout
- Returns status (healthy/degraded/unhealthy), uptime, cache metrics
- Update TryConnect() to use health check instead of ping
- Add 'bd daemon --health' CLI command with JSON output
- Track cache hits/misses for metrics
- Unhealthy daemon triggers automatic fallback to direct mode
- Health check completes in <2 seconds

Amp-Thread-ID: https://ampcode.com/threads/T-1a4889f3-77cf-433a-a704-e1c383929f48
Co-authored-by: Amp <amp@ampcode.com>

internal/rpc/client.go

@@ -17,7 +17,7 @@ type Client struct {
 }
 
 // TryConnect attempts to connect to the daemon socket
-// Returns nil if no daemon is running
+// Returns nil if no daemon is running or unhealthy
 func TryConnect(socketPath string) (*Client, error) {
 	if _, err := os.Stat(socketPath); os.IsNotExist(err) {
 		if os.Getenv("BD_DEBUG") != "" {
@@ -40,14 +40,28 @@ func TryConnect(socketPath string) (*Client, error) {
 		timeout:    30 * time.Second,
 	}
 
-	if err := client.Ping(); err != nil {
+	health, err := client.Health()
+	if err != nil {
 		if os.Getenv("BD_DEBUG") != "" {
-			fmt.Fprintf(os.Stderr, "Debug: ping failed: %v\n", err)
+			fmt.Fprintf(os.Stderr, "Debug: health check failed: %v\n", err)
 		}
 		conn.Close()
 		return nil, nil
 	}
 
+	if health.Status == "unhealthy" {
+		if os.Getenv("BD_DEBUG") != "" {
+			fmt.Fprintf(os.Stderr, "Debug: daemon unhealthy: %s\n", health.Error)
+		}
+		conn.Close()
+		return nil, nil
+	}
+
+	if os.Getenv("BD_DEBUG") != "" {
+		fmt.Fprintf(os.Stderr, "Debug: connected to daemon (status: %s, uptime: %.1fs, cache: %d)\n",
+			health.Status, health.Uptime, health.CacheSize)
+	}
+
 	return client, nil
 }
 
@@ -131,6 +145,21 @@ func (c *Client) Ping() error {
 	return nil
 }
 
+// Health sends a health check request to verify the daemon is healthy
+func (c *Client) Health() (*HealthResponse, error) {
+	resp, err := c.Execute(OpHealth, nil)
+	if err != nil {
+		return nil, err
+	}
+
+	var health HealthResponse
+	if err := json.Unmarshal(resp.Data, &health); err != nil {
+		return nil, fmt.Errorf("failed to unmarshal health response: %w", err)
+	}
+
+	return &health, nil
+}
+
 // Create creates a new issue via the daemon
 func (c *Client) Create(args *CreateArgs) (*Response, error) {
 	return c.Execute(OpCreate, args)