feat: per-phase timings of the frame path in the log

One log line per phase every PHASE_LOG_EVERY samples (default 100, 0 = off):
mean and max of wait_frames, align, convert, each JPEG/PNG encoding,
colormap, depth_stats, base64, json and ws_send. Meant for the measurement
on PC2 via `docker logs` (optimize-streams R01): where a capture spends its
~130 ms of CPU is not known yet.

capture() moves its numpy conversion into _frame_from() unchanged, only so
the block can be timed; _depth_colormap() likewise wraps _jet_colormap().

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

tests/test_phase_timing.py

@@ -0,0 +1,46 @@
+"""PhaseTimer: per-phase mean/max, logged and reset every N samples."""
+
+import logging
+
+import pytest
+
+from src.backend.services.phase_timing import PhaseStats, PhaseTimer, summary_line
+
+
+def test_summary_line_mean_and_max_in_ms():
+    line = summary_line("align", PhaseStats(count=4, total_s=0.2, max_s=0.08))
+    assert line == "phase align: n=4 mean=50.0 ms max=80.0 ms"
+
+
+def test_logs_and_resets_every_n_samples(caplog):
+    timer = PhaseTimer(log_every=3)
+    with caplog.at_level(logging.INFO, logger="src.backend.services.phase_timing"):
+        for seconds in (0.010, 0.030, 0.020, 0.005):
+            timer.record("wait_frames", seconds)
+    lines = [r.getMessage() for r in caplog.records]
+    assert lines == ["phase wait_frames: n=3 mean=20.0 ms max=30.0 ms"]
+
+
+def test_phases_are_counted_separately(caplog):
+    timer = PhaseTimer(log_every=2)
+    with caplog.at_level(logging.INFO, logger="src.backend.services.phase_timing"):
+        timer.record("a", 0.001)
+        timer.record("b", 0.001)
+        timer.record("a", 0.003)
+    assert [r.getMessage() for r in caplog.records] == ["phase a: n=2 mean=2.0 ms max=3.0 ms"]
+
+
+def test_zero_turns_it_off(caplog):
+    timer = PhaseTimer(log_every=0)
+    with caplog.at_level(logging.INFO, logger="src.backend.services.phase_timing"):
+        for _ in range(5):
+            timer.record("x", 0.001)
+    assert caplog.records == []
+
+
+def test_phase_records_even_when_the_block_raises():
+    timer = PhaseTimer(log_every=1000)
+    with pytest.raises(RuntimeError):
+        with timer.phase("encode"):
+            raise RuntimeError("boom")
+    assert timer._stats["encode"].count == 1