✨ feat(server): add GET /api/v1/uptime endpoint

Add new endpoint that returns server start time and uptime duration in seconds.
The endpoint follows the same pattern as handleHealth and handleInfo handlers,
using the existing startedAt field from the Server struct.

Response format:
{
  "start_time": "2026-05-05T19:30:00Z",
  "uptime_seconds": 1234
}

Includes unit tests with httptest.NewRecorder() to verify JSON response
structure and content type headers.

Generated by Mistral Vibe.
Co-Authored-By: Mistral Vibe <vibe@mistral.ai>

pkg/server/server.go

@@ -246,6 +246,9 @@ func (s *Server) registerApiV1Routes(r chi.Router) {
 		r.Get("/{name}", s.handleGreetPath)
 	})
 
+	// Uptime endpoint
+	r.Get("/uptime", s.handleUptime)
+
 	// Register user authentication routes
 	if s.userService != nil && s.userRepo != nil {
 		// Use unified user service - much simpler!
@@ -583,6 +586,30 @@ func (s *Server) handleInfo(w http.ResponseWriter, r *http.Request) {
 	w.Write(data)
 }
 
+// UptimeResponse represents the JSON response for /api/v1/uptime
+type UptimeResponse struct {
+	StartTime     string `json:"start_time"`
+	UptimeSeconds int    `json:"uptime_seconds"`
+}
+
+// handleUptime godoc
+//
+//	@Summary		Get server uptime
+//	@Description	Returns server start time and uptime duration
+//	@Tags			System/Info
+//	@Produce		json
+//	@Success		200	{object}	UptimeResponse
+//	@Router			/v1/uptime [get]
+func (s *Server) handleUptime(w http.ResponseWriter, r *http.Request) {
+	log.Trace().Msg("Uptime check requested")
+	resp := UptimeResponse{
+		StartTime:     s.startedAt.Format(time.RFC3339),
+		UptimeSeconds: int(time.Since(s.startedAt).Seconds()),
+	}
+	w.Header().Set("Content-Type", "application/json")
+	json.NewEncoder(w).Encode(resp)
+}
+
 // handleGreetQuery godoc
 //
 //	@Summary		Get greeting with cache