Fix SEC-04: add security headers to API

- Add globalSecurityHeaders middleware wrapping root handler
- Sets X-Content-Type-Options, Strict-Transport-Security, Cache-Control
  on all responses (API and UI)
- Add tests verifying headers on /v1/health and /v1/auth/login

Security: API responses previously lacked HSTS, nosniff, and
cache-control headers. The new middleware applies these universally.
Headers are safe for all content types and do not conflict with
the UI's existing securityHeaders middleware.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

internal/server/server_test.go

@@ -594,3 +594,47 @@ func TestRenewToken(t *testing.T) {
 		t.Error("old token should be revoked after renewal")
 	}
 }
+
+// TestSecurityHeadersOnAPIResponses verifies that the global security-headers
+// middleware (SEC-04) sets X-Content-Type-Options, Strict-Transport-Security,
+// and Cache-Control on all API responses, not just the UI.
+func TestSecurityHeadersOnAPIResponses(t *testing.T) {
+	srv, _, _, _ := newTestServer(t)
+	handler := srv.Handler()
+
+	wantHeaders := map[string]string{
+		"X-Content-Type-Options":    "nosniff",
+		"Strict-Transport-Security": "max-age=63072000; includeSubDomains",
+		"Cache-Control":             "no-store",
+	}
+
+	t.Run("GET /v1/health", func(t *testing.T) {
+		rr := doRequest(t, handler, "GET", "/v1/health", nil, "")
+		if rr.Code != http.StatusOK {
+			t.Fatalf("status = %d, want 200", rr.Code)
+		}
+		for header, want := range wantHeaders {
+			got := rr.Header().Get(header)
+			if got != want {
+				t.Errorf("%s = %q, want %q", header, got, want)
+			}
+		}
+	})
+
+	t.Run("POST /v1/auth/login", func(t *testing.T) {
+		createTestHumanAccount(t, srv, "sec04-user")
+		rr := doRequest(t, handler, "POST", "/v1/auth/login", map[string]string{
+			"username": "sec04-user",
+			"password": "testpass123",
+		}, "")
+		if rr.Code != http.StatusOK {
+			t.Fatalf("status = %d, want 200; body: %s", rr.Code, rr.Body.String())
+		}
+		for header, want := range wantHeaders {
+			got := rr.Header().Get(header)
+			if got != want {
+				t.Errorf("%s = %q, want %q", header, got, want)
+			}
+		}
+	})
+}