TUI shows and enforces login for local LLM providers (no ChatGPT, no API key), blocking usage

What version of Codex is running?

commit: 97f995a749a2cd8b4edf68d59edf6d18f4363825

Which model were you using?

local LLM providers (no ChatGPT, no API key)

What platform is your computer?

any

What steps can reproduce the bug?

1) Configure Codex to use a local LLM provider that does not require OpenAI authentication (e.g., LM Studio).
2) Ensure you are not signed in with ChatGPT and do not have an OpenAI API key set.
3) Launch the TUI.
4) Observe that the onboarding/login screen is shown and you cannot proceed without choosing an auth method.

What is the expected behavior?

When the selected model provider does not require OpenAI authentication, the TUI should skip the login step entirely and allow immediate use of the local provider, even if the user is not authenticated and has no API key.

What do you see instead?

The TUI shows the login screen and effectively blocks progress when not authenticated, even for providers that do not require OpenAI authentication.

Additional information

After commit 97f995a749a2cd8b4edf68d59edf6d18f4363825, the TUI onboarding incorrectly displays (and effectively enforces) the login screen even when using a local LLM provider that does not require OpenAI authentication (e.g., LM Studio). As a result, users who neither sign in with ChatGPT nor set an API key can no longer use Codex with local models.