Go: implement Encode (embeddings) in Google Gemini driver (#14682)

### What problem does this PR solve?

- Implements the `Encode` method in the Google Gemini driver, which was
previously a stub returning `not implemented`
- Uses the `google.golang.org/genai` SDK's `EmbedContent` API, which
routes to the `batchEmbedContents` endpoint internally — all texts are
sent in a single request
- Adds `text-embedding-004` (max 2048 tokens) to
`conf/models/google.json`
- Response values are `[]float32` from the SDK and are cast to
`[]float64` to satisfy the `ModelDriver` interface

## Files changed

- `internal/entity/models/google.go` — full `Encode` implementation
- `conf/models/google.json` — adds `text-embedding-004` embedding model

### Type of change

- [x] New Feature (non-breaking change which adds functionality)

conf/models/google.json

@@ -18,6 +18,13 @@
         "default_value": true,
         "clear_thinking": true
       }
+    },
+    {
+      "name": "text-embedding-004",
+      "max_tokens": 2048,
+      "model_types": [
+        "embedding"
+      ]
     }
   ],
   "features": {

internal/entity/models/google.go

@@ -212,9 +212,60 @@ func (z *GoogleModel) ChatStreamlyWithSender(modelName string, messages []Messag
 	return err
 }
 
-// Encode encodes a list of texts into embeddings
+// Encode generates embeddings for a batch of texts using the Gemini embeddings API.
+// The SDK routes to batchEmbedContents internally, so all texts are sent in one request.
 func (z *GoogleModel) Encode(modelName *string, texts []string, apiConfig *APIConfig, embeddingConfig *EmbeddingConfig) ([][]float64, error) {
-	return nil, fmt.Errorf("not implemented")
+	if apiConfig == nil || apiConfig.ApiKey == nil || *apiConfig.ApiKey == "" {
+		return nil, fmt.Errorf("api key is required")
+	}
+	if modelName == nil || *modelName == "" {
+		return nil, fmt.Errorf("model name is required")
+	}
+	if len(texts) == 0 {
+		return nil, fmt.Errorf("texts is empty")
+	}
+
+	ctx, cancel := context.WithTimeout(context.Background(), nonStreamCallTimeout)
+	defer cancel()
+
+	client, err := genai.NewClient(ctx, &genai.ClientConfig{
+		APIKey:  *apiConfig.ApiKey,
+		Backend: genai.BackendGeminiAPI,
+	})
+	if err != nil {
+		return nil, fmt.Errorf("failed to create client: %w", err)
+	}
+
+	contents := make([]*genai.Content, len(texts))
+	for i, text := range texts {
+		contents[i] = genai.NewContentFromText(text, genai.RoleUser)
+	}
+
+	var cfg *genai.EmbedContentConfig
+	if embeddingConfig != nil && embeddingConfig.Dimension > 0 {
+		dim := int32(embeddingConfig.Dimension)
+		cfg = &genai.EmbedContentConfig{OutputDimensionality: &dim}
+	}
+
+	resp, err := client.Models.EmbedContent(ctx, *modelName, contents, cfg)
+	if err != nil {
+		return nil, fmt.Errorf("failed to embed content: %w", err)
+	}
+
+	if len(resp.Embeddings) != len(texts) {
+		return nil, fmt.Errorf("expected %d embeddings, got %d", len(texts), len(resp.Embeddings))
+	}
+
+	result := make([][]float64, len(resp.Embeddings))
+	for i, emb := range resp.Embeddings {
+		vec := make([]float64, len(emb.Values))
+		for j, v := range emb.Values {
+			vec[j] = float64(v)
+		}
+		result[i] = vec
+	}
+
+	return result, nil
 }
 
 func (z *GoogleModel) ListModels(apiConfig *APIConfig) ([]string, error) {
@@ -245,7 +296,8 @@ func (z *GoogleModel) Balance(apiConfig *APIConfig) (map[string]interface{}, err
 }
 
 func (z *GoogleModel) CheckConnection(apiConfig *APIConfig) error {
-	return fmt.Errorf("no such method")
+	_, err := z.ListModels(apiConfig)
+	return err
 }
 
 // Rerank calculates similarity scores between query and documents