Support AWS Bedrock as a provider backend

Hi Codex Action team,

First of all, thank you for building and maintaining codex-action.

We are currently using anthropics/claude-code-action, mainly because it supports running Claude through AWS Bedrock. However, in our workflow it has been quite slow, and we would strongly prefer to use openai/codex-action with GPT-5.5 instead.

Would you consider adding support for AWS Bedrock as a provider/backend, similar to how anthropics/claude-code-action supports Bedrock?

Our ideal workflow would be something like:

- uses: openai/codex-action@v1
  with:
    provider: bedrock
    model: gpt-5.5
    # AWS Bedrock-related configuration

The main motivation is that many teams already have AWS Bedrock set up for enterprise access, security controls, IAM-based authentication, billing, and compliance. Supporting Bedrock would make it much easier for those teams to adopt codex-action without changing their existing cloud/provider setup.

Benefits:

• Enable teams already using AWS Bedrock to adopt codex-action
• Allow use of GPT-5.5 in GitHub Actions workflows through existing enterprise AWS infrastructure
• Provide an alternative to claude-code-action for teams that need Bedrock support
• Potentially improve speed and reliability for workflows currently bottlenecked by other code-action integrations

Thanks for considering this feature request.

Start with the GitHub Actions workflow configuration shown in the issue and trace how codex-action currently selects its provider and model. Define the AWS Bedrock configuration and authentication requirements, then verify that a workflow can select Bedrock and complete a GPT-5.5 run through the existing action.