fix(climate): write mode-correct setpoints and stop REST reverting live state

Two independent bugs made a second change (e.g. adjusting the target
temperature right after switching cool -> heat) fail to take, and made
Home Assistant settle back on a previous state while DKN Cloud NA showed
the correct one.

Wrong setpoint key on write:

_writable_temperature_property_for_mode() ignored its hvac_mode argument
and resolved the key from real_mode/mode in the cached device payload.
That payload still describes the pre-change state, so a heat setpoint was
emitted as setpoint_air_cool: the unit switched to heat but the heat
setpoint never moved. The same defect broke AUTO in steady state, where
real_mode=cool made the write target setpoint_air_cool while the read
used setpoint_air_auto, so the value could never appear to change.

target_temperature() and writable_target_temperature_key() now accept the
mode the caller intends, and that mode takes priority over anything in the
device payload. Device-reported modes remain a fallback only for payloads
that do not expose the requested mode's setpoint.

async_set_temperature() no longer re-sends power+mode; async_set_hvac_mode()
already sent them, and the stale-cache condition guarding the resend was
always true. It now waits (bounded) for the cloud to echo the mode before
sending the setpoint, matching the ensure_mode ordering the smoke test uses.

REST snapshot reverting live state:

The coordinator merged {**existing, **device}, letting the lagging REST
/installations snapshot win over live Socket.IO pushes. Once the socket
confirmed a write, _reconcile_optimistic dropped the overlay, leaving
nothing to stop the next poll from reverting the state.

Socket-pushed values are now tracked per device and applied after the REST
payload. They are discarded when the socket session changes, since updates
may have been missed while it was down and REST becomes authoritative again.

Also report hvac_action and target_temperature against the effective
(optimistic-aware) mode so the action cannot contradict the reported mode
while a change propagates.

Co-authored-by: anthropic/claude-opus-5

custom_components/dkncloudna/api.py

@@ -65,6 +65,10 @@ class DknCloudNaClient:
         self._socket_refresh_callback: Callable[[], Awaitable[None]] | None = None
         self._last_command_ack: dict[str, Any] | None = None
         self._recent_socket_events: deque[dict[str, Any]] = deque(maxlen=20)
+        # Incremented on every successful Socket.IO connection so consumers can
+        # tell that live state accumulated from the previous session is no
+        # longer trustworthy and must be re-synced from REST.
+        self.socket_session = 0
 
     def clear_password(self) -> None:
         """Discard password from memory after token exchange."""
@@ -194,6 +198,7 @@ class DknCloudNaClient:
         self._socket = sio
         self._socket_installations = installation_ids
         self._socket_token = self.token
+        self.socket_session += 1
         return True
 
     async def _ensure_socket_ready_for_write_locked(self, installation_id: str) -> None: