Capture errno before it can be clobbered, warn when no UDP address is valid, and give the reboot test timing headroom

tests/integration/fixtures/api_reboot_timeout_after_authenticated_disconnect.yaml

@@ -2,6 +2,6 @@ esphome:
   name: api-reboot-test
 host:
 api:
-  reboot_timeout: 0.5s  # Very short timeout for fast testing
+  reboot_timeout: 2s  # Headroom to connect and authenticate a client first
 logger:
   level: DEBUG

tests/integration/test_api_reboot_timeout.py

@@ -59,6 +59,6 @@ async def test_api_reboot_timeout_after_authenticated_disconnect(
         async with api_client_connected() as client:
             await client.device_info()
         try:
-            await asyncio.wait_for(reboot_future, timeout=2.0)
+            await asyncio.wait_for(reboot_future, timeout=5.0)
         except TimeoutError:
             pytest.fail("Device did not reboot within expected timeout")