When using custom/local model_provider we still need to either login with ChatGPT or provide API key

What version of Codex is running?

0.47.0

What subscription do you have?

API

Which model were you using?

gpt-5 / gpt-5-codex

What platform is your computer?

Darwin 24.6.0 arm64 arm

What issue are you seeing?

When using custom/local model_provider we still need to either login with ChatGPT or provide API key.
It works even if we add a bogus API key, like "ABC" but doesn't make sense to require one.

What steps can reproduce the bug?

Run codex with custom/local model_provider

What is the expected behavior?

We should have a new option "3. Use custom model provider" (which doesn't do anything, just uses the custom model provider defined in config) next to the current ones "1. Login with ChatGPT", "2. Use API key"

Additional information

_No response_