Smooth battery percent readings before computing drop-rate steps

A 1M-ohm divider (way over the ~10k source impedance the ESP32 ADC's
sample-and-hold expects) doesn't always misfire in isolation -- short
bursts of a few consecutive bad readings, and multi-reading drifts,
both slip past the existing step-level MAD outlier rejection since the
steps between two bad readings in the same burst look ordinary. Add a
Hampel-filter smoothing pass (local-neighborhood MAD, same statistical
approach as the existing outlier rejection) ahead of it.

server/tests/test_battery_estimate.py

@@ -1,11 +1,10 @@
-"""_reject_outlier_drops -- the outlier-rejection pass in the battery
-remaining-time estimate (see routers/common.py's battery_estimate_s).
-Pure function, no DB/HTTP -- (recency_weight, drop_pct) pairs in,
-filtered pairs out."""
+"""_reject_outlier_drops and _smooth_percents -- the two outlier-rejection
+passes in the battery remaining-time estimate (see routers/common.py's
+battery_estimate_s). Pure functions, no DB/HTTP."""
 
 from __future__ import annotations
 
-from app.routers.common import _reject_outlier_drops
+from app.routers.common import _reject_outlier_drops, _smooth_percents
 
 
 def _steps(drops: list[float]) -> list[tuple[int, float]]:
@@ -69,3 +68,37 @@ def test_never_filters_down_to_nothing():
     steps = _steps([1, 1, 1, 1, 10, 10, 10, 10])
     kept = _reject_outlier_drops(steps)
     assert len(kept) > 0
+
+
+def test_smooth_corrects_isolated_spike():
+    percents = [70, 70, 70, 70, 70, 90, 70, 70, 70, 70, 70]
+    smoothed = _smooth_percents(percents)
+    assert smoothed[5] == 70
+    assert smoothed[:5] == percents[:5]
+    assert smoothed[6:] == percents[6:]
+
+
+def test_smooth_corrects_short_burst():
+    """The shape seen in production: several consecutive corrupted
+    reports (a 1M-ohm divider glitching for a few reports in a row, not
+    just one) spliced into an otherwise flat run. A step computed
+    between two of these looks like an ordinary small change, which is
+    exactly why _reject_outlier_drops alone can't catch this shape."""
+    percents = [53, 53, 53, 53, 41, 40, 40, 42, 53, 53, 53, 53]
+    smoothed = _smooth_percents(percents)
+    assert smoothed[4:8] == [53, 53, 53, 53]
+    assert smoothed[:4] == percents[:4]
+    assert smoothed[8:] == percents[8:]
+
+
+def test_smooth_leaves_gradual_legitimate_trend_alone():
+    """A slow, steady climb (recharge) or decline spread over many
+    reports is a real trend, not a local glitch -- each reading is close
+    to its own neighborhood's median, so nothing should be flagged."""
+    percents = list(range(80, 60, -2))  # 80, 78, 76, ... steady discharge
+    assert _smooth_percents(percents) == percents
+
+
+def test_smooth_identical_readings_untouched():
+    percents = [50] * 12
+    assert _smooth_percents(percents) == percents