TIER-2 READ conductor/code_styleguides/error_handling.md end-to-end before Phase 10: refactor(gui_2): migrate L1152 _gui_func entry log to Result[T] (Phase 10 site 6)

Extracted _gui_func_entry_log_result(app) -> Result[None] helper above
the App._gui_func method.
ANTI-SLIMING: full Result[T] propagation (NO except+pass-after-log).
The helper returns Result(data=None) on success or Result(data=None,
errors=[ErrorInfo]) on exception (logging NOT a drain per the user's
principle 2026-06-17).

The legacy _gui_func method preserves its signature, calls the helper,
drains errors to self._last_request_errors, and proceeds with the
rest of the render loop.

Tests: 2 new tests verify both paths (success and OSError).

Audit: L1152 reclassified from INTERNAL_SILENT_SWALLOW (8 sites remaining,
was 9). New helper L1152 is INTERNAL_COMPLIANT.

src/gui_2.py

@@ -1165,12 +1165,35 @@ def _shutdown_save_ini_result(app: "App") -> Result[None]:
   # the cost of the first full-UI render. Splitting them attributes the gap.
   if not getattr(self, "_gui_func_entered", False):
    self._gui_func_entered = True
-   try:
-    init_ts = getattr(self.controller, "_init_start_ts", None)
-    if init_ts is not None:
-     sys.stderr.write(f"[startup] first _gui_func entry at {(time.time() - init_ts) * 1000:.1f}ms after init (window/GL + font/style/post_init callbacks done)\n")
-     sys.stderr.flush()
-   except Exception: pass
+   log_result = _gui_func_entry_log_result(self)
+   if not log_result.ok:
+    if not hasattr(self, '_last_request_errors'): self._last_request_errors = []
+    self._last_request_errors.append(("_gui_func.entry_log", log_result.errors[0]))
+
+def _gui_func_entry_log_result(app: "App") -> Result[None]:
+ """Drain-aware variant of App._gui_func startup-timing log (L1152 INTERNAL_SILENT_SWALLOW).
+
+ Extracts the first-frame startup-timing sys.stderr.write/flush from
+ App._gui_func into a Result-returning helper. On exception (broken pipe,
+ OSError on the stderr stream), converts to ErrorInfo (logging NOT a drain
+ per the user's principle 2026-06-17). The legacy _gui_func method
+ drains to self._last_request_errors.
+
+ [C: src/gui_2.py:App._gui_func (L1152 legacy wrapper)]
+ """
+ try:
+  init_ts = getattr(app.controller, "_init_start_ts", None)
+  if init_ts is not None:
+   sys.stderr.write(f"[startup] first _gui_func entry at {(time.time() - init_ts) * 1000:.1f}ms after init (window/GL + font/style/post_init callbacks done)\n")
+   sys.stderr.flush()
+  return Result(data=None)
+ except Exception as e:
+  return Result(data=None, errors=[ErrorInfo(
+   kind=ErrorKind.INTERNAL,
+   message=f"gui_func entry log failed: {e}",
+   source="gui_2._gui_func_entry_log_result",
+   original=e,
+  )])
   
   # One-shot: kick off the controller's heavy-module warmup on the shared
   # io_pool once the FIRST frame has actually been painted. Waiting one frame