perf(push): drop per-entry cache fsync; let long runs profile themselves

The cache fsynced every payload and manifest -- two per entry, ~18 ms, and a
push publishes one entry per question (~22,000 on a WordPress plugin). A
read already rejects any entry whose manifest receipt, payload size or
payload SHA-256 does not check, so a torn write is a miss, never a wrong
answer; the fsyncs bought nothing the verification does not.

The broader problem: three quadratic walls in this replay were found one
per two-hour run, because all were Python bookkeeping between engine calls
and the only record was the engine log. `OUSAST_SAMPLE_PROFILE=<path>`
starts an in-process sampler that rewrites the hottest stacks every 30 s,
so a run killed at its deadline still names where its time went. The host
cannot ptrace the container, hence in-process. The replay harness turns it
on per case.

Co-Authored-By: Claude Opus 5.5 (1M context) <[email protected]>
Claude-Session: https://claude.ai/code/session_01EmM1j46qgKMh3zqD1QMwEo

tests/test_profiling.py

@@ -0,0 +1,28 @@
+"""The in-process sampler leaves a readable profile behind, including for a process killed mid-run."""
+
+import time
+
+from openultrasast import profiling
+
+
+def _busy_quadratic(n: int) -> int:
+    seen: list[int] = []
+    for i in range(n):
+        if i not in seen:
+            seen.append(i)
+    return len(seen)
+
+
+def test_the_sampler_names_the_function_that_holds_the_time(tmp_path, monkeypatch):
+    target = tmp_path / "profile.txt"
+    monkeypatch.delenv(profiling.ENV, raising=False)
+    assert profiling.start() is None  # off unless asked for
+    assert profiling.start(str(target), interval=0.002, flush=0.2) is not None
+    deadline = time.monotonic() + 1.5
+    while time.monotonic() < deadline:
+        _busy_quadratic(3000)
+    time.sleep(0.3)
+    text = target.read_text()
+    assert text.startswith("samples ")
+    self_section = text.split("self (executing):")[1]
+    assert "_busy_quadratic" in self_section.splitlines()[1], self_section[:300]