[Windows] Pets cannot be dragged in Codex 26.715.4045, including default pet

Codex version: 26.715.4045
Platform: Windows desktop
Display setup: One display, 1920×1080
Previous working version: 26.715.2305

Actual:
No pet can be dragged. This affects the built-in default pet and every
custom pet. Restarting Codex, resetting placement, switching pets, and
forcing non-native rendering did not help.

Expected:
The pet should become interactive when hovered and move when dragged.

Diagnostics:
The pet overlay remains click-through (WS_EX_TRANSPARENT). It begins
non-interactive and does not transition out of mouse passthrough, so
pointer-down and drag-start events never reach the renderer.

This appears to be a shared Windows overlay regression rather than a pet
asset or monitor-position problem. macOS works because it uses a separate
native cursor/drag bridge.

Related: #21359, but this reproduction does not require a secondary display.

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