fix(availability): F3 — any usable transport keeps the entities up (t40)

Reported from a live install: with ADB enabled but unreachable and a paired,
healthy protocol transport, the media player went unavailable even though the
protocol still served power/app/volume.

The old rule was ``manager.connected or manager.awake is not None or not
manager.available`` — i.e. "a configured ADB manager that is down ⇒ the whole
entity is down" (t5-F2), which ignored transport B entirely. The ladder is now:

* protocol transport wired and not reported unreachable — usable;
* or ADB connected — usable;
* or fresh wake data (the poller has spoken) — usable;
* or a passive manager (no ADB configured at all) — usable, because nothing to
  transport is not a broken transport.

Unavailable only when a CONFIGURED transport is actively down and no usable data
exists. One implementation, ``entity_available`` (media_player.py), is used by the
media player, the remote (whose ladder previously duplicated a weaker version of
this rule) and the diagnostics payload.

Diagnostics grew ``transport.entity_available`` plus ``adb.configured`` so a
support dump answers "why is my entity unavailable?" — the ladder inputs and its
verdict are now in the same place.

Pinned by tests: the exact user case (ADB configured+down, protocol up ⇒
available), all-down (⇒ unavailable), wake-data rescue, connected ADB without a
protocol, the passive manager, a configured-but-down transport with no data, the
remote following the same ladder, and the diagnostics verdict.

Verified: 310 passed / 2 skipped, 311 passed / 1 skipped (androidtvremote2),
16 passed in the HA drift suite, ruff clean.

custom_components/nvidia_shield/media_player.py

@@ -153,6 +153,35 @@ async def _migrate_legacy_unique_id(hass, entry) -> None:
     _LOGGER.info("P5-1: legacy unique_id %r migrated to %r", legacy, new_id)
 
 
+def entity_available(manager: ShieldConnectionManager | None) -> bool:
+    """Is ANY usable transport healthy for this entry? (t40 live install)
+
+    The single ladder behind ``media_player.available``, ``remote.available``
+    and the diagnostics payload, so the three cannot disagree:
+
+    * the protocol transport is wired and has not reported the device
+      unreachable — it serves power/app/volume even when ADB is down;
+    * or ADB is connected (live state data);
+    * or fresh wake data exists (the poller has spoken at least once);
+    * or the manager is passive (no ADB configured at all): nothing to
+      transport is not a broken transport.
+
+    Unavailable only when a CONFIGURED transport is actively down and no usable
+    data exists. The t5-F2 rule ("an ADB manager that is down means unreliable
+    state") took the whole entity down while a healthy paired protocol transport
+    was still serving commands — the reported defect.
+    """
+    if not isinstance(manager, ShieldConnectionManager):
+        return True
+    if manager.protocol_active and manager.is_available is not False:
+        return True
+    if manager.connected:
+        return True
+    if manager.awake is not None:
+        return True
+    return not manager.available
+
+
 def resolve_app_name(
     package: str | None,
     app_name_map,
@@ -225,15 +254,13 @@ class NvidiaShieldMediaPlayer(MediaPlayerEntity):
 
     @property
     def available(self) -> bool:
-        """The bridge entities stay functional without ADB (passive manager).
+        """Available while ANY usable transport is healthy (t40 live install).
 
-        Unavailable only while an active ADB manager is down — its data is
-        unreliable until the watchdog reconnects (t5-F2).
+        ADB enabled but unreachable no longer takes the entity down: a paired,
+        available protocol transport still serves power/app/volume. The ladder
+        is shared with the remote and diagnostics (``entity_available``).
         """
-        manager = getattr(self._entry, "runtime_data", None)
-        if not isinstance(manager, ShieldConnectionManager):
-            return True
-        return manager.connected or manager.awake is not None or not manager.available
+        return entity_available(getattr(self._entry, "runtime_data", None))
 
     @property
     def _jellyfin_entity(self) -> str | None: