[Feature]: Add Vertex AI Gemini provider

## Summary

Add support for using Google Gemini models through Vertex AI. QwenPaw currently supports Gemini via the Gemini Developer API, but users who require Google Cloud billing, IAM/auth, governance, regional routing, or Vertex AI access cannot configure that path directly.

## Component(s) Affected

- [x] Core / Backend (app, agents, config, providers, utils, local_models)
- [ ] Console (frontend web UI)
- [ ] Channels (DingTalk, Feishu, QQ, Discord, iMessage, etc.)
- [ ] Skills
- [ ] CLI
- [x] Documentation (website)
- [x] Tests
- [ ] CI/CD
- [ ] Scripts / Deploy

## Problem / Motivation

QwenPaw has a built-in Google Gemini provider, but it appears to target the Gemini Developer API / AI Studio API-key flow.

From the current implementation, `GeminiProvider` creates a `google-genai` client with `api_key=...`, and the built-in provider base URL is `https://generativelanguage.googleapis.com`. I did not find provider configuration for Vertex AI fields such as `vertexai=True`, Google Cloud `project`, `location`, or Application Default Credentials.

This makes it difficult for users who need to use Gemini through Vertex AI, for example because of:

- Google Cloud billing and quota management
- IAM / Application Default Credentials
- enterprise governance requirements
- regional model access through Vertex AI
- existing GCP infrastructure policies

## Proposed Solution

Add a separate built-in provider for Vertex AI Gemini, for example `vertex-gemini`, rather than changing the existing `gemini` provider.

A separate provider would keep the current Gemini Developer API behavior unchanged for users who use AI Studio / API-key auth, while adding a clear path for Vertex AI users.

Possible implementation direction:

- Add a provider class such as `VertexGeminiProvider`.
- Use Google Gen AI SDK Vertex mode, for example:
- `genai.Client(vertexai=True, project=..., location=...)`
- or environment variables:
- `GOOGLE_GENAI_USE_VERTEXAI=true`
- `GOOGLE_CLOUD_PROJECT=`
- `GOOGLE_CLOUD_LOCATION=`
- Register the provider in `ProviderManager`.
- Include at least one default Vertex-compatible Gemini model.
- Add unit tests for client initialization, connection check, model discovery or configured models, and model connection check.
- Update `website/public/docs/models.*.md` with Vertex AI setup instructions.
- Include connection test evidence and a chat screenshot in the PR.

Open questions for maintainers:

1. Would a native `vertex-gemini` built-in provider be acceptable?
2. Should Vertex AI support be a separate provider, or an option inside the existing `gemini` provider?
3. Should QwenPaw expose `project` and `location` as provider config fields, or rely on environment variables / ADC?
4. Would maintainers prefer using Vertex AI’s OpenAI-compatible Chat Completions endpoint instead of native `google-genai` Vertex mode?

## Alternatives Considered

Use the existing `gemini` provider:

This does not seem sufficient because it currently uses API-key auth and the Gemini Developer API endpoint, not Vertex AI project/location auth.

Use a custom OpenAI-compatible provider:

Vertex AI provides an OpenAI-compatible Chat Completions endpoint, but it uses Google Cloud authentication / short-lived OAuth tokens rather than a normal static API key. That may not fit QwenPaw’s current custom provider configuration cleanly without extra token refresh handling or a proxy.

Modify the existing `gemini` provider:

This might work, but it could make the current Gemini API-key flow more complex. A separate provider seems safer and clearer for users.

## Additional Context

Relevant current code:

- `src/qwenpaw/providers/gemini_provider.py`
- `GeminiProvider._client()` currently creates `genai.Client(api_key=self.api_key, ...)`
- `get_chat_model_instance()` passes `api_key=self.api_key` to `GeminiChatModel`

- `src/qwenpaw/providers/provider_manager.py`
- built-in Gemini provider ID: `gemini`
- provider name: `Google Gemini`
- base URL: `https://generativelanguage.googleapis.com`

Relevant docs:

- Google Gen AI SDK supports Vertex AI with `vertexai=True`, `project`, and `location`, or with environment variables:
- `GOOGLE_GENAI_USE_VERTEXAI=true`
- `GOOGLE_CLOUD_PROJECT`
- `GOOGLE_CLOUD_LOCATION`

Google Gen AI SDK docs:
https://googleapis.github.io/python-genai/

Vertex AI OpenAI-compatible endpoint docs:
https://docs.cloud.google.com/vertex-ai/generative-ai/docs/start/openai

## Willing to Contribute

- [x] I am willing to open a PR for this feature (after discussion).