feat(startup_profiler): add module-level singleton + live stderr logging

- startup_profiler: StartupProfiler = StartupProfiler() at module bottom
  so sloppy.py can import it without circular imports.
- phase() context manager now writes a [startup] <name>: <ms>ms line to
  stderr in its finally block. Live visibility of every measured phase.

src/startup_profiler.py

@@ -1,4 +1,5 @@
 import time
+import sys
 from contextlib import contextmanager
 from dataclasses import dataclass, field
 from typing import Any, Iterator
@@ -33,6 +34,11 @@ class StartupProfiler:
   finally:
    p.end_ts = time.perf_counter()
    self._phases.append(p)
+   try:
+    sys.stderr.write(f"[startup] {name}: {(p.end_ts - p.start_ts) * 1000.0:.1f}ms\n")
+    sys.stderr.flush()
+   except Exception:
+    pass
 
  def snapshot(self) -> dict[str, Any]:
   phases: dict[str, dict[str, float]] = {}
@@ -52,3 +58,6 @@ class StartupProfiler:
 
  def reset(self) -> None:
   self._phases.clear()
+
+
+startup_profiler: StartupProfiler = StartupProfiler()