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
@@ -6,14 +7,14 @@ from typing import Any, Iterator
 
 @dataclass
 class _Phase:
- name: str
+ name:     str
  start_ts: float
- end_ts: float = 0.0
+ end_ts:   float = 0.0
 
 
 @dataclass
 class StartupProfiler:
- _phases: list[_Phase] = field(default_factory=list)
+ _phases:  list[_Phase] = field(default_factory=list)
  _enabled: bool = True
 
  def enable(self) -> None:
@@ -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]] = {}
@@ -40,15 +46,18 @@ class StartupProfiler:
   for p in self._phases:
    duration_ms = max(0.0, (p.end_ts - p.start_ts) * 1000.0) if p.end_ts else 0.0
    phases[p.name] = {
-    "start_ts": p.start_ts,
+    "start_ts":    p.start_ts,
     "duration_ms": round(duration_ms, 3),
    }
    total += duration_ms
   return {
-   "phases": phases,
+   "phases":   phases,
    "total_ms": round(total, 3),
-   "count": len(phases),
+   "count":    len(phases),
   }
 
  def reset(self) -> None:
   self._phases.clear()
+
+
+startup_profiler: StartupProfiler = StartupProfiler()