Move LogHandler from app.py to log_handler.py (no behavior change)

Step 9 of the gui/app.py + gui/preview.py structural refactor. Pure
copy: the Qt-aware logging.Handler that bridges the booru logger to
the in-app QTextEdit log panel moves to its own module. app.py grows
another shim line so any internal `LogHandler(...)` reference (the
single one in BooruApp._setup_ui) keeps resolving through the module
namespace. Shim removed in commit 14.

booru_viewer/gui/app.py

@@ -51,28 +51,6 @@ from .settings import SettingsDialog
 log = logging.getLogger("booru")
 
 
-class LogHandler(logging.Handler, QObject):
-    """Logging handler that emits to a QTextEdit."""
-
-    log_signal = Signal(str)
-
-    def __init__(self, widget: QTextEdit) -> None:
-        logging.Handler.__init__(self)
-        QObject.__init__(self)
-        self._widget = widget
-        self.log_signal.connect(self._append)
-        self.setFormatter(logging.Formatter("%(asctime)s  %(levelname)-5s  %(message)s", datefmt="%H:%M:%S"))
-
-    def emit(self, record: logging.LogRecord) -> None:
-        msg = self.format(record)
-        self.log_signal.emit(msg)
-
-    def _append(self, msg: str) -> None:
-        self._widget.append(msg)
-        sb = self._widget.verticalScrollBar()
-        sb.setValue(sb.maximum())
-
-
 class AsyncSignals(QObject):
     """Signals for async worker results."""
     search_done = Signal(list)
@@ -3598,3 +3576,4 @@ def run() -> None:
 
 # -- Refactor compatibility shims (deleted in commit 14) --
 from .search_state import SearchState  # re-export for refactor compat
+from .log_handler import LogHandler  # re-export for refactor compat

booru_viewer/gui/log_handler.py

@@ -0,0 +1,30 @@
+"""Qt-aware logging handler that emits log lines to a QTextEdit."""
+
+from __future__ import annotations
+
+import logging
+
+from PySide6.QtCore import QObject, Signal
+from PySide6.QtWidgets import QTextEdit
+
+
+class LogHandler(logging.Handler, QObject):
+    """Logging handler that emits to a QTextEdit."""
+
+    log_signal = Signal(str)
+
+    def __init__(self, widget: QTextEdit) -> None:
+        logging.Handler.__init__(self)
+        QObject.__init__(self)
+        self._widget = widget
+        self.log_signal.connect(self._append)
+        self.setFormatter(logging.Formatter("%(asctime)s  %(levelname)-5s  %(message)s", datefmt="%H:%M:%S"))
+
+    def emit(self, record: logging.LogRecord) -> None:
+        msg = self.format(record)
+        self.log_signal.emit(msg)
+
+    def _append(self, msg: str) -> None:
+        self._widget.append(msg)
+        sb = self._widget.verticalScrollBar()
+        sb.setValue(sb.maximum())