Pet overlay forces desktop switch and is mispositioned above the dock on Windows

<img width="236" height="105" alt="Image" src="https://github.com/user-attachments/assets/4da2fd0c-dea8-4b0a-b4f6-47f9bc22b33b" />

What version of the Codex App are you using (From “About Codex” dialog)?

Codex 26.429.30905

What subscription do you have?

business plan

What platform is your computer?

Windows

What issue are you seeing?

When the Codex pet is active, its overlay is not positioned cleanly above the dock/taskbar. On virtual desktop switches, Codex can also force focus back to the desktop where it is running. The pet appears to overlap the dock area instead of staying anchored above it.

What steps can reproduce the bug?

1. Open Codex on Windows with the pet visible.
2. Switch to another virtual desktop.
3. Trigger a Codex notification or update while the pet is still active.
4. Observe that the active desktop switches back and the pet overlay sits incorrectly over the dock/taskbar.

What is the expected behavior?

The pet should stay visually anchored above the dock/taskbar and should not force the active desktop to switch.

Additional information

This appears separate from the WSL custom-pet loading issue. There is also a related desktop-switching report on macOS, but this report is specifically about the pet overlay position and desktop behavior on Windows.