[ENHANCEMENT] Multiple Codex Provider Logins

[megamorphg]

Problem (one or two sentences)

Currently, it is not possible to have multiple OpenAI Codex API Providers.
After clicking sign-out, it signs out on all configuration profiles.

Context (who is affected and when)

I have a work Codex and a personal Codex. I'd like to switch between the two, especially when I bump into limitations.

Desired behavior (conceptual, not technical)

It is useful to have multiple Codex providers or providers that require Sign in.

Constraints / preferences (optional)

No response

Request checklist

• I've searched existing Issues and Discussions for duplicates
• This describes a specific problem with clear context and impact

Zoo Code Task Links (optional)

No response

Acceptance criteria (optional)

No response

Proposed approach (optional)

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Trade-offs / risks (optional)

No response