Fix race in ESPHome entity test (#111179)

This test relied on the event loop overhead. Change it
to listen for the state to change instead

tests/components/esphome/test_entity.py

@@ -1,4 +1,5 @@
 """Test ESPHome binary sensors."""
+import asyncio
 from collections.abc import Awaitable, Callable
 from typing import Any
 from unittest.mock import AsyncMock
@@ -21,8 +22,13 @@ from homeassistant.const import (
     STATE_ON,
     STATE_UNAVAILABLE,
 )
-from homeassistant.core import HomeAssistant
+from homeassistant.core import HomeAssistant, callback
 from homeassistant.helpers import entity_registry as er
+from homeassistant.helpers.event import (
+    EventStateChangedData,
+    async_track_state_change_event,
+)
+from homeassistant.helpers.typing import EventType
 
 from .conftest import MockESPHomeDevice
 
@@ -215,7 +221,19 @@ async def test_entities_removed_after_reload(
     )
 
     assert await hass.config_entries.async_setup(entry.entry_id)
+    on_future = hass.loop.create_future()
+
+    @callback
+    def _async_wait_for_on(event: EventType[EventStateChangedData]) -> None:
+        if event.data["new_state"].state == STATE_ON:
+            on_future.set_result(None)
+
+    async_track_state_change_event(
+        hass, ["binary_sensor.test_mybinary_sensor"], _async_wait_for_on
+    )
     await hass.async_block_till_done()
+    async with asyncio.timeout(2):
+        await on_future
 
     assert mock_device.entry.entry_id == entry_id
     state = hass.states.get("binary_sensor.test_mybinary_sensor")