Skip the dial delay when no inbound path waits, keep dial-out alive when the listener fails, check the socket results this PR made meaningful, and cover the clean reboot branch

tests/integration/fixtures/api_reboot_timeout_after_authenticated_disconnect.yaml

@@ -0,0 +1,7 @@
+esphome:
+  name: api-reboot-test
+host:
+api:
+  reboot_timeout: 0.5s  # Very short timeout for fast testing
+logger:
+  level: DEBUG

tests/integration/test_api_reboot_timeout.py

@@ -5,7 +5,7 @@ import re
 
 import pytest
 
-from .types import RunCompiledFunction
+from .types import APIClientConnectedFactory, RunCompiledFunction
 
 
 @pytest.mark.asyncio
@@ -35,3 +35,30 @@ async def test_api_reboot_timeout(
             pytest.fail("Device did not reboot within expected timeout")
 
     # Test passes if we get here - reboot was detected
+
+
+@pytest.mark.asyncio
+async def test_api_reboot_timeout_after_authenticated_disconnect(
+    yaml_config: str,
+    run_compiled: RunCompiledFunction,
+    api_client_connected: APIClientConnectedFactory,
+) -> None:
+    """An authenticated disconnect resets the flag; the clean branch reboots."""
+    loop = asyncio.get_running_loop()
+    reboot_future = loop.create_future()
+    reboot_pattern = re.compile(r"No clients; rebooting")
+
+    def check_output(line: str) -> None:
+        """Check output for reboot message."""
+        if not reboot_future.done() and reboot_pattern.search(line):
+            reboot_future.set_result(True)
+
+    async with run_compiled(yaml_config, line_callback=check_output):
+        # An authenticated session refreshes the watchdog and clears the
+        # unauthenticated flag the harness probe set
+        async with api_client_connected() as client:
+            await client.device_info()
+        try:
+            await asyncio.wait_for(reboot_future, timeout=2.0)
+        except TimeoutError:
+            pytest.fail("Device did not reboot within expected timeout")