plan/10: Add /api/stats endpoint and dashboard stats badge

- Add GetStats handler returning agent counts, plan/task/queue breakdowns
- Wire GET /api/stats route in api/main.go
- Add stats_test.go with handler unit tests
- Add StatsWidget.tsx component (idle/working agents, plan/task counts)
- Add DashboardHeader.tsx displaying stats badge in the dashboard header

api/handlers/stats.go

@@ -0,0 +1,93 @@
+package handlers
+
+import (
+	"github.com/gin-gonic/gin"
+)
+
+type StatsResponse struct {
+	AgentCount    int            `json:"agent_count"`
+	WorkingAgents int            `json:"working_agents"`
+	PlanCounts    map[string]int `json:"plan_counts"`
+	TaskCounts    map[string]int `json:"task_counts"`
+	QueueCounts   map[string]int `json:"queue_counts"`
+}
+
+func (h *Handler) GetStats(c *gin.Context) {
+	// Get total agent count
+	agentCount, err := h.db.Query(`SELECT COUNT(*) FROM agents`)
+	if err != nil {
+		c.JSON(500, gin.H{"error": err.Error()})
+		return
+	}
+	defer agentCount.Close()
+	var totalAgents int
+	if agentCount.Next() {
+		agentCount.Scan(&totalAgents)
+	}
+
+	// Get working agent count
+	workingAgents, err := h.db.Query(`SELECT COUNT(*) FROM agents WHERE status = 'working'`)
+	if err != nil {
+		c.JSON(500, gin.H{"error": err.Error()})
+		return
+	}
+	defer workingAgents.Close()
+	var workingAgentCount int
+	if workingAgents.Next() {
+		workingAgents.Scan(&workingAgentCount)
+	}
+
+	// Get plan counts by status
+	planCounts := make(map[string]int)
+	rows, err := h.db.Query(`SELECT status, COUNT(*) FROM plans GROUP BY status`)
+	if err != nil {
+		c.JSON(500, gin.H{"error": err.Error()})
+		return
+	}
+	defer rows.Close()
+	for rows.Next() {
+		var status string
+		var count int
+		rows.Scan(&status, &count)
+		planCounts[status] = count
+	}
+
+	// Get task counts by status
+	taskCounts := make(map[string]int)
+	rows, err = h.db.Query(`SELECT status, COUNT(*) FROM tasks GROUP BY status`)
+	if err != nil {
+		c.JSON(500, gin.H{"error": err.Error()})
+		return
+	}
+	defer rows.Close()
+	for rows.Next() {
+		var status string
+		var count int
+		rows.Scan(&status, &count)
+		taskCounts[status] = count
+	}
+
+	// Get queue counts by status
+	queueCounts := make(map[string]int)
+	rows, err = h.db.Query(`SELECT status, COUNT(*) FROM director_queue GROUP BY status`)
+	if err != nil {
+		c.JSON(500, gin.H{"error": err.Error()})
+		return
+	}
+	defer rows.Close()
+	for rows.Next() {
+		var status string
+		var count int
+		rows.Scan(&status, &count)
+		queueCounts[status] = count
+	}
+
+	// Return stats
+	c.JSON(200, StatsResponse{
+		AgentCount:    totalAgents,
+		WorkingAgents: workingAgentCount,
+		PlanCounts:    planCounts,
+		TaskCounts:    taskCounts,
+		QueueCounts:   queueCounts,
+	})
+}