test(backend): cover poll_ca_cert timeout paths for diff-coverage gate

Add tests for the three uncovered paths introduced by the poll_ca_cert
extraction: the timeout + sleep branches in backend/util, and the
TimeoutError → GatewayError and TimeoutError → die() conversions in the
macOS and Firecracker callers.

tests/unit/test_backend_util.py

@@ -0,0 +1,29 @@
+"""Unit: shared cross-backend helpers in backend/util.py."""
+
+from __future__ import annotations
+
+import unittest
+from unittest.mock import patch
+
+from bot_bottle.backend import util as backend_util
+
+
+class TestPollCaCert(unittest.TestCase):
+    def test_returns_pem_on_first_success(self) -> None:
+        result = backend_util.poll_ca_cert(lambda: "PEM", timeout=1.0)
+        self.assertEqual("PEM", result)
+
+    def test_raises_timeout_error_when_cert_never_appears(self) -> None:
+        with self.assertRaises(TimeoutError):
+            backend_util.poll_ca_cert(lambda: None, timeout=0.0)
+
+    def test_polls_until_cert_appears(self) -> None:
+        responses = iter([None, None, "-----BEGIN CERTIFICATE-----\n"])
+        with patch("bot_bottle.backend.util.time.sleep") as mock_sleep:
+            result = backend_util.poll_ca_cert(lambda: next(responses), timeout=5.0)
+        self.assertTrue(result.startswith("-----BEGIN CERTIFICATE-----"))
+        self.assertEqual(2, mock_sleep.call_count)
+
+
+if __name__ == "__main__":
+    unittest.main()

tests/unit/test_firecracker_infra_vm.py

@@ -71,6 +71,16 @@ class TestSshGatewayTransport(unittest.TestCase):
             t.exec(["mkdir", "-p", "/git-gate"])
 
 
+class TestGatewayCaPem(unittest.TestCase):
+    def test_dies_when_cert_never_appears(self) -> None:
+        from subprocess import CompletedProcess
+        infra = infra_vm.InfraVm(vm=None, guest_ip="10.0.0.1", private_key=Path("/k"))
+        with patch.object(infra_vm.subprocess, "run",
+                          return_value=CompletedProcess([], 1, stdout="", stderr="")), \
+             self.assertRaises(SystemExit):
+            infra.gateway_ca_pem(timeout=0)
+
+
 class TestRegistryVolume(unittest.TestCase):
     def test_reuses_existing_volume(self):
         import tempfile

tests/unit/test_macos_infra.py

@@ -153,6 +153,14 @@ class TestCaCertPem(unittest.TestCase):
         argv = mod.run_container_argv.call_args.args[0]
         self.assertEqual(["container", "exec", "bot-bottle-mac-infra", "cat"], argv[:4])
 
+    def test_raises_gateway_error_when_cert_never_appears(self) -> None:
+        from bot_bottle.backend.macos_container.gateway import GatewayError
+        svc = MacosInfraService(repo_root=Path("/r"))
+        with patch(f"{_INFRA}.container_mod") as mod:
+            mod.run_container_argv.return_value = _fail()
+            with self.assertRaises(GatewayError):
+                svc.ca_cert_pem(timeout=0)
+
 
 class TestProbeControlPlane(unittest.TestCase):
     def test_returns_url_when_running(self) -> None: