Decrease event loop latency by binding time.monotonic to loop.time directly (#98288)

* Decrease event loop latency by binding time.monotonic to loop.time directly

This is a small improvment to decrease event loop latency. While the goal is
is to reduce Bluetooth connection time latency, everything using asyncio
is a bit more responsive as a result.

* relo per comments

* fix too fast by adding resolution, ensure monotonic time is patchable by freezegun

* fix test that freezes time too late and has a race loop

tests/patch_time.py

@@ -2,8 +2,9 @@
 from __future__ import annotations
 
 import datetime
+import time
 
-from homeassistant import util
+from homeassistant import runner, util
 from homeassistant.util import dt as dt_util
 
 
@@ -12,5 +13,11 @@ def _utcnow() -> datetime.datetime:
     return datetime.datetime.now(datetime.UTC)
 
 
+def _monotonic() -> float:
+    """Make monotonic patchable by freezegun."""
+    return time.monotonic()
+
+
 dt_util.utcnow = _utcnow  # type: ignore[assignment]
 util.utcnow = _utcnow  # type: ignore[assignment]
+runner.monotonic = _monotonic  # type: ignore[assignment]