Track radiator lag across relay changes

The lag proxy was reset to the new relay command at every relay change
and after any skipped interval, so it read 1.0 straight after ON and 0.0
straight after OFF. This disabled the lag model around every boiler
cycle: on a synthetic lagged plant cycled by a hysteresis thermostat the
learner's heat gain came out 34% low (0.079 vs 0.12) and the loss term
43% low, and the optimizer started post-transition plans from the wrong
lag.

Track the lag at every poll with a valid relay state, independently of
room sensors. Integrate a single change between polls at its
last_changed time. For ambiguous cases (round trip between polls, relay
outage, restart, clock jump) restart from time-in-state with an explicit
error half-width, and learn only once it is at most 0.1 (about 32 min
after an HA restart). The same synthetic test now learns 0.1195/0.00389
(true 0.12/0.004).

Expose heat_lag, heat_lag_uncertainty and sample_result on Status so
users can see why a poll was or was not learned. The HA test fixture
relay now has an hour-old timestamp; a new test covers a freshly
written relay state.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

tests/ha/test_lifecycle.py

@@ -146,3 +146,17 @@ async def test_startup_missing_inputs_then_recovery(hass, entry):
     await coordinator.async_refresh()
     assert coordinator.data["status"] == "learning"
     assert coordinator.data["samples"] == 0
+
+
+async def test_freshly_written_relay_state_defers_learning(hass, entry, inputs, freezer):
+    """After an HA restart the relay's last_changed is new, so radiator lag is unknown."""
+    hass.states.async_set("switch.boiler", "on")
+    coordinator = await setup(hass, entry)
+    assert coordinator.data["heat_lag"] == 0.5
+    assert coordinator.data["heat_lag_uncertainty"] == 0.5
+    future = dt_util.utcnow() + timedelta(minutes=5, seconds=1)
+    freezer.move_to(future)
+    async_fire_time_changed(hass, future)
+    await hass.async_block_till_done()
+    assert coordinator.data["sample_result"] == "lag_uncertain"
+    assert coordinator.learners["sensor.room"].count == 0