修复 Studio 失败测试并新增合并门禁

把丢失的 box 录像放回 apps/studio/tests/data/，修掉第 3 节 3–10 号与两处过时测试桩，
注册 timing 标记并让根目录收集零错误；新增 tools/gate.ps1 与可选的 pre-push 钩子。
验证：studio 524 通过 19 跳过、shared 467 通过 18 跳过、ui_check 632 项 0 失败、gate.ps1 退出码 0。
细节见 docs/test-repair-plan.zh.md。

apps/studio/tests/_studio_helpers.py

@@ -0,0 +1,57 @@
+"""Plain helpers the studio UI tests share, importable without a ``tests`` package.
+
+These four functions used to live in ``conftest.py`` and were imported as
+``from tests.conftest import ...``. That import only worked when pytest ran with
+``apps/studio`` in ``sys.path`` (or as the working directory): run from the
+repository root, the ``tests`` directory of *any* product could be shadowed, and
+the suite could not be collected at all. A module beside the tests, with the
+tests' own directory on ``sys.path``, has none of that ambiguity.
+
+Fixtures stay in ``conftest.py`` (pytest discovers them); only the functions a
+test imports by name live here.
+"""
+
+from __future__ import annotations
+
+
+def visible_descendants(widget):
+    """Yield every visible descendant widget of ``widget``."""
+    for child in widget.findChildren(object):
+        if not hasattr(child, "isVisible") or not hasattr(child, "geometry"):
+            continue
+        if child.isVisible():
+            yield child
+
+
+def show_window(window, size):
+    """Show a window at ``size`` and flush pending Qt events."""
+    from PySide6.QtWidgets import QApplication
+
+    window.resize(*size)
+    window.show()
+    QApplication.processEvents()
+    return window
+
+
+def running_window(make_window):
+    """Return a running window backed by a controllable test worker."""
+    import ui_check
+
+    window = show_window(
+        make_window(sensor_type="box", source_mode="camera"),
+        (1440, 880),
+    )
+    stuck = ui_check._StuckWorker()
+    window._ensure_workers = lambda: None
+    window._box_worker = stuck
+    window._finger_worker = stuck
+    window._start_run()
+    window._run_timer.stop()
+    window._set_phase("running")
+    return window, stuck
+
+
+def finish_run(window, stuck):
+    """Stop a test run and release its controllable worker."""
+    window._stop_run(reason="user_stop")
+    stuck.release()