Fix OAuth: Add CLAUDE_CODE_OAUTH_TOKEN env var and fix API key handling

- Add CLAUDE_CODE_OAUTH_TOKEN to environment variables for base action
- Don't pass 'use-oauth' as anthropic_api_key to base action
- This should allow Claude Code to detect and use OAuth properly

action.yml

@@ -124,7 +124,7 @@ runs:
         mcp_config: ${{ steps.prepare.outputs.mcp_config }}
         use_bedrock: ${{ inputs.use_bedrock }}
         use_vertex: ${{ inputs.use_vertex }}
-        anthropic_api_key: ${{ inputs.anthropic_api_key }}
+        anthropic_api_key: ${{ inputs.anthropic_api_key != 'use-oauth' && inputs.anthropic_api_key || '' }}
         claude_code_oauth_token: ${{ steps.prepare.outputs.claude_oauth_token }}
       env:
         # Core configuration
@@ -139,6 +139,8 @@ runs:
         USE_VERTEX: ${{ inputs.use_vertex }}
         # Only set ANTHROPIC_API_KEY if not using OAuth
         ANTHROPIC_API_KEY: ${{ inputs.anthropic_api_key != 'use-oauth' && inputs.anthropic_api_key || '' }}
+        # OAuth token for Claude Code
+        CLAUDE_CODE_OAUTH_TOKEN: ${{ steps.prepare.outputs.claude_oauth_token }}
 
         # GitHub token for repository access
         GITHUB_TOKEN: ${{ steps.prepare.outputs.GITHUB_TOKEN }}