✨ feat(server): add /api/healthz endpoint with rich health info (#20)

Adds Kubernetes-style /api/healthz endpoint with status/version/uptime_seconds/timestamp.

Non-breaking — /api/health preserved. Includes unit test (passes locally) and BDD scenario (validated by CI).

Généré ~95% en autonomie par Mistral Vibe via workspace ICM ~/Work/Vibe/workspaces/healthz-feature/.

Co-authored-by: Gabriel Radureau <arcodange@gmail.com>
Co-committed-by: Gabriel Radureau <arcodange@gmail.com>

pkg/server/healthz_test.go

@@ -0,0 +1,43 @@
+package server
+
+import (
+	"context"
+	"encoding/json"
+	"net/http"
+	"net/http/httptest"
+	"testing"
+
+	"dance-lessons-coach/pkg/config"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestHandleHealthz(t *testing.T) {
+	// Setup
+	cfg := &config.Config{}
+	s := NewServer(cfg, context.Background())
+
+	// Create request
+	req := httptest.NewRequest(http.MethodGet, "/api/healthz", nil)
+	w := httptest.NewRecorder()
+
+	// Call handler
+	s.handleHealthz(w, req)
+
+	// Check status code
+	assert.Equal(t, http.StatusOK, w.Code)
+
+	// Check content type
+	assert.Equal(t, "application/json", w.Header().Get("Content-Type"))
+
+	// Decode response
+	var resp HealthzResponse
+	err := json.NewDecoder(w.Body).Decode(&resp)
+	assert.NoError(t, err)
+
+	// Assert fields
+	assert.Equal(t, "healthy", resp.Status)
+	assert.NotEmpty(t, resp.Version)
+	assert.GreaterOrEqual(t, resp.UptimeSeconds, int64(0))
+	assert.NotZero(t, resp.Timestamp)
+}