feat: add Azure OpenAI provider support

[cdowellmdb]

Summary

• add an Azure-aware provider path to write-proxy-config, letting the action write either the local proxy stanza or an Azure config

• detect which credentials are provided at runtime so we only start the Responses proxy when an OpenAI key is present, otherwise wire Azure directly

• document the new Azure inputs, including the automatic /openai normalization to avoid 404s

• Closes Azure support? #38

• Closes How to connect to Azure OpenAI Service? #28

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[cdowellmdb]

I have read the CLA Document and I hereby sign the CLA

[bolinfest]

I feel like the better fix here is for me to update https://github.com/openai/codex/tree/main/codex-rs/responses-api-proxy to be configurable such that it can forward requests to an Azure endpoint. What do you think?

[bolinfest]

@cdowellmdb Specifically, I believe that CODEX_AZURE_API_KEY is, at a minimum, in memory as an env var for the node "${{ github.action_path }}/dist/main.js" run-codex-exec invocation in run_codex, so it can be read back out of procfs by Codex even though sudo has been dropped.

[bolinfest]

Here's a draft PR for updating the proxy to support this use case: openai/codex#6129

[cdowellmdb]

@bolinfest I like your approach better, thanks for kicking off both PRs in codex and codex-action!

I'll follow those threads with @pakrym-oai, appreciate your help on this.