The interactions interface is incompatible with the Vertex AI Express mode

The interactions (NextGen) interface is incompatible with the Vertex AI Express mode (API Key authentication).

When using Express mode, the client initializer enforces a mutual exclusion between the API key and the project/location parameters. Because the project and location are missing, the SDK fails to construct the required Vertex AI resource path (/v1beta1/projects/{project}/locations/{location}/interactions). Instead, it falls back to a default path (/v1beta1/interactions) on the Gemini Developer API server, which does not exist and results in a 404 Not Found error.

To use the interactions interface, you must use the standard GCP Credentials authentication mode by providing a project, location, and valid Google Cloud credentials.

使用 Vertex AI Express mode 和 API-key authentication 重现 Interactions 接口，然后检查报告中描述的客户端初始化器和资源路径构造。完成的标准是：Express mode 配置能够到达所需的基于项目/位置的 Vertex AI interactions 路径，而不是返回 404 的默认 Gemini Developer API 路径。

由索引模型根据 Issue 内容生成。