plan/10: Add /api/stats endpoint and dashboard stats badge (#2)

Adds GET /api/stats endpoint with agent/plan/task/queue counts, stats widget in dashboard header, and Go test coverage.

api/main.go

@@ -73,6 +73,7 @@ func main() {
 		// Agents
 		api.GET("/agents", h.ListAgents)
 		api.PATCH("/agents/:id", h.UpdateAgent)
+		api.GET("/agents/:id/next-task", h.NextTask)
 
 		// Director Queue
 		api.GET("/queue", h.ListQueue)
@@ -91,6 +92,12 @@ func main() {
 		// System / Settings
 		api.GET("/system/claude-mode", h.GetClaudeMode)
 		api.POST("/system/claude-mode", h.SetClaudeMode)
+		api.GET("/system/claude-usage", h.GetClaudeUsage)
+		api.POST("/system/claude-usage", h.SetClaudeUsage)
+		api.POST("/system/claude-kill-switch", h.ClaudeKillSwitch)
+
+		// Stats
+		api.GET("/stats", h.GetStats)
 	}
 
 	// WebSocket