Feature request: OpenAI ChatGPT subscription (alongside the API-key path)

[guberm]

Summary

Please add an option to use an existing OpenAI ChatGPT subscription in OpenWorker, without requiring a separate OpenAI API key and usage billing.

This would be similar to the Claude subscription-auth request in #402, while keeping the current API-key flow available.

Proposed behavior

• Add OpenAI Subscription as an authentication option in the provider settings.
• Use an official OpenAI-supported OAuth/subscription authentication flow.
• Let users sign in, sign out, reconnect, and see the current connection status.
• Keep API-key authentication as a separate fallback.
• Do not scrape browser sessions or ask users to paste cookies or access tokens manually.
• If OpenAI does not officially allow subscription use by third-party clients, show a clear explanation and keep this option unavailable.

Acceptance criteria

• A user can select OpenAI Subscription and complete sign-in through the supported OpenAI flow.
• OpenWorker can start a session using models available through that subscription.
• Authentication errors and expired sessions produce actionable reconnect guidance.
• Tokens are stored securely and are never written to logs.
• Existing OpenAI API-key users are unaffected.

Why

Many users already pay for ChatGPT Plus, Pro, Business, or another OpenAI subscription and would prefer to use that subscription in OpenWorker instead of managing separate API credentials and billing.