Feature Request: Add quick switching for Codex Pets

What variant of Codex are you using?

App

What feature would you like to see?

Codex Pets are a delightful and useful companion feature. They are not just cosmetic: the floating overlay helps me keep track of active Codex work, including whether a thread is running, waiting for input, or ready for review.

Currently, I can choose a pet from Settings → Appearance → Pets, and I can wake or tuck away the pet with /pet or the command palette. However, switching between pets still requires going back into Settings. This becomes inconvenient when users have multiple built-in or custom pets.

I would like Codex to support quick pet switching without opening Settings.

Suggested design:

Add a right-click menu on the floating pet overlay with:
Switch Pet…
Next Pet
Previous Pet
Favorite Pets
Allow users to bind shortcuts for Next Pet and Previous Pet.
Switching should preserve the current overlay position, current task state, and active thread. It should only change the pet appearance.
It should work for both built-in pets and custom pets loaded from the local Codex home.

Why this matters:

Codex Pets encourage users to create and collect custom pets. Once users have several pets, they naturally want to switch based on project, mood, task type, or workspace. A quick switcher would make the pet system feel more complete and would make custom pets much more usable.

Acceptance criteria:

A pet can be switched in two interactions or fewer.
Built-in and custom pets appear in the same switcher.
Switching does not interrupt running Codex tasks.
The current overlay position and visibility state are preserved.
Missing or invalid custom pet assets show a clear error instead of silently failing.

Thanks for building Codex Pets — this feature would make them much more practical and enjoyable to use.

Additional information

_No response_