### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

A bare pip/uv install of `litellm[proxy]` with a `vertex_ai/*` model in `model_list` starts the proxy cleanly, but **every request then fails with a 500** whose root cause is a raw `ModuleNotFoundError: No module named 'google'` raised from `vertex_llm_base.py` (`from google.auth.credentials import TokenState`).

`google-auth` is not part of the `proxy` extra, and nothing validates it at startup even though the config declares Vertex models that can only authenticate through `google.auth`.

Why this is surprising from a user's perspective:

- The `proxy` extra **does** ship the equivalent auth dependency for the other major clouds — `boto3` (Bedrock/SigV4) and `azure-identity` are both in `[project.optional-dependencies].proxy` — so Vertex is the only major cloud whose auth dependency is missing from a `litellm[proxy]` install. - The Docker image pre-installs `google-cloud-aiplatform` (via `proxy-runtime`), so the failure only hits pip/uv users, e.g. anyone following the "Use Claude Code with Non-Anthropic Models" tutorial with a Gemini/Vertex …