feat(api): add support for HEAD requests to /healthz endpoint

- Refactored `/healthz` handler to support `HEAD` requests alongside `GET`.
- Updated tests to include validation for `HEAD` requests with expected status and empty body.

Closes: #2929

internal/api/server.go

@@ -319,9 +319,16 @@ func NewServer(cfg *config.Config, authManager *auth.Manager, accessManager *sdk
 // setupRoutes configures the API routes for the server.
 // It defines the endpoints and associates them with their respective handlers.
 func (s *Server) setupRoutes() {
-	s.engine.GET("/healthz", func(c *gin.Context) {
+	healthzHandler := func(c *gin.Context) {
+		if c.Request.Method == http.MethodHead {
+			c.Status(http.StatusOK)
+			return
+		}
+
 		c.JSON(http.StatusOK, gin.H{"status": "ok"})
-	})
+	}
+	s.engine.GET("/healthz", healthzHandler)
+	s.engine.HEAD("/healthz", healthzHandler)
 
 	s.engine.GET("/management.html", s.serveManagementControlPanel)
 	openaiHandlers := openai.NewOpenAIAPIHandler(s.handlers)