[Fix] OpenAI provider section missing when ChatGPT is also connected

[roomote-roomote]

Opened on behalf of Matt Rubens. Follow up by mentioning @roomote-roomote, in the web UI, or in Slack.

Related issue

N/A — internal bug report from Slack.

Why this PR exists

• A maintainer explicitly invited this PR in the linked issue or discussion
• I am a maintainer / this is internal Roomote work

What changed

When a ChatGPT subscription was connected, every openai/ model was listed under ChatGPT (subscription), which hid the OpenAI provider section even if an OpenAI API key was also connected.

Model lists now keep the OpenAI section when an OpenAI key is present. ChatGPT-only connections still group openai/ models under ChatGPT. Runtime auth still prefers the subscription when both are configured (existing Inference Providers notice is unchanged).

How it was tested

• Package Vitest: types model-provider-config plus web ModelSettingsSection and ModelSelect client tests
• Pre-push gates: oxlint, residual web/worker ESLint, check-types:fast, knip
• Browser proof of the dual-connected admin settings state was not captured: the sandbox cannot yield a real dual-connected ChatGPT OAuth + OpenAI key fixture for that UI path

Checklist

• The PR title follows the repo convention: [Fix], [Feat], [Improve], [Refactor], [Docs], or [Chore] followed by a user-facing description
• This PR is small and scoped to one change
• pnpm lint and pnpm check-types pass locally
• I added tests or included a clear manual validation note above
• I removed secrets, tokens, private keys, and customer data from code, logs, and screenshots
• If this change should appear in the changelog, I ran pnpm changeset

[roomote-roomote]

No code issues found. See task

_{Reviewed db0f02d}