How to configure google vertex with desktop app?

[xlc]

Question

Google Vertex is using credential json file, not API key
For OpenRouter, BYOK, it is clear I should provide such JSON file to it, not the case here
For reference, this is OpenRouter screen

[github-actions]

This issue might be a duplicate of existing issues. Please check:

• Which Google API key to use? Vertex AI API or an API key created in Goggle AI Studio? #3586: Which Google API key to use? Vertex AI API or an API key created in Goggle AI Studio?
• When use vertex models (like gemini 3 pro perview) no session name generated. #5097: When use vertex models (like gemini 3 pro preview) no session name generated
• Vertex AI: BadRequestError 'instructions: Extra inputs are not permitted' when running agents #4282: Vertex AI: BadRequestError 'instructions: Extra inputs are not permitted' when running agents
• Supporting Vertex-based models using google auth #272: Supporting Vertex-based models using google auth

Feel free to ignore if none of these address your specific case.