Windows pet overlay clicks pass through; initial drag sometimes jumps away from cursor

On OpenAI.Codex Windows Store package 26.901.6511.0, the animated pet cannot reliably receive clicks. Clicks target the window behind it. Immediately after waking, dragging may start, but the pet jumps away while the cursor remains in place. Changing pets, hiding/waking, and fully restarting did not resolve it.

Single 1920x1080 display at 100%, window DPI 96. During a user-positioned hover over the visible pet, WindowFromPoint resolved to a child of the underlying primary Codex window, not the visible/enabled pet overlay. Overlay exstyle was 0x280088, without WS_EX_TRANSPARENT. Saved pet anchor was (1415,659), cursor was (1458,710), and the overlay bounds were (1083,0)-(1855,1080).

Please investigate overlay input shape / transparent-window hit testing and renderer-to-native drag coordinates. Exact root cause remains unverified. The app's Store updater reported NoUpdates at 09:58:26 China Standard Time on 2026-09-15.

Start by reproducing the Windows Store package behavior with the stated 1920x1080, 100% DPI setup, then trace the overlay's native hit testing and renderer-to-native drag coordinate path. Done means clicks reach the visible pet overlay and the first drag keeps the pet under the cursor after waking, without relying on changes to the underlying Codex window.