fix(grok): enable free prompt cache for Responses function tools

Reuse applyGrokFreeMessagesFunctionToolCacheRoute on native /v1/responses
and the Grok WS HTTP bridge so Free OAuth requests with client function
tools get the same mixed-tools cache route as the Messages bridge
(append/convert web_search and x_search).

Also dedupe: Grok Build already declares function tools named web_search,
so naive append caused "Duplicate tool names: web_search". Convert those
function entries to native tool types and skip duplicates.

Only Free OAuth accounts (isKnownGrokFreeAccount); paid/unknown unchanged.

backend/internal/service/openai_gateway_grok.go

@@ -61,6 +61,12 @@ func (s *OpenAIGatewayService) forwardGrokResponses(
 	if err != nil {
 		return nil, fmt.Errorf("apply grok prompt cache identity: %w", err)
 	}
+	// Free OAuth + client function tools: reuse Messages mixed-tools cache route
+	// (append web_search/x_search so xAI does not force non-cacheable build-free).
+	patchedBody, err = applyGrokFreeMessagesFunctionToolCacheRoute(patchedBody, body, account, cacheIdentity)
+	if err != nil {
+		return nil, fmt.Errorf("apply grok Free function-tool cache route: %w", err)
+	}
 
 	token, _, err := s.getRequestCredential(ctx, c, account)
 	if err != nil {

backend/internal/service/openai_gateway_grok_cache.go

@@ -102,8 +102,8 @@ func isGrokRequestContext(c *gin.Context) bool {
 // Free OAuth requests without native search tools are routed by xAI to the
 // non-cacheable build-free model. For otherwise tool-free requests, add the
 // native tools with tool_choice=none: this selects the cache-capable tier
-// without allowing an actual search. Explicit client tools are handled by the
-// narrower Messages-only mixed-tools policy below.
+// without allowing an actual search. Explicit client function tools are handled by
+// applyGrokFreeMessagesFunctionToolCacheRoute (Messages bridge and native Responses).
 func applyGrokResponsesCacheIdentity(body, intentSourceBody []byte, identity string, injectFreeTierTools bool) ([]byte, error) {
 	identity = strings.TrimSpace(identity)
 	if identity == "" {
@@ -263,17 +263,35 @@ func appendMissingGrokFreeCacheNativeTools(body []byte) ([]byte, error) {
 		toolType := strings.TrimSpace(tool.Get("type").String())
 		switch toolType {
 		case "function":
-			if !tool.IsObject() || strings.TrimSpace(tool.Get("name").String()) == "" || tool.Get("function").Exists() {
+			name := strings.TrimSpace(tool.Get("name").String())
+			if !tool.IsObject() || name == "" || tool.Get("function").Exists() {
 				return body, nil
 			}
+			// Grok Build may declare search as function tools. Convert to native
+			// entries so Free OAuth stays cache-capable without duplicate names.
+			if name == "web_search" || name == "x_search" {
+				if present[name] {
+					continue
+				}
+				raw, err := json.Marshal(map[string]string{"type": name})
+				if err != nil {
+					return nil, err
+				}
+				merged = append(merged, raw)
+				present[name] = true
+				continue
+			}
 			hasFunction = true
+			merged = append(merged, json.RawMessage(tool.Raw))
 		case "web_search", "x_search":
-			// Native tools may already be present when this helper is retried.
+			if present[toolType] {
+				continue
+			}
+			merged = append(merged, json.RawMessage(tool.Raw))
+			present[toolType] = true
 		default:
 			return body, nil
 		}
-		merged = append(merged, json.RawMessage(tool.Raw))
-		present[toolType] = true
 	}
 	if !hasFunction {
 		return body, nil

backend/internal/service/openai_ws_http_bridge.go

@@ -201,6 +201,11 @@ func (s *OpenAIGatewayService) proxyOpenAIWSHTTPBridgeTurn(
 			releaseUpstreamCtx()
 			return nil, fmt.Errorf("apply grok prompt cache identity: %w", err)
 		}
+		body, err = applyGrokFreeMessagesFunctionToolCacheRoute(body, grokIntentSourceBody, account, grokCacheIdentity)
+		if err != nil {
+			releaseUpstreamCtx()
+			return nil, fmt.Errorf("apply grok Free function-tool cache route: %w", err)
+		}
 		upstreamReq, err = buildGrokResponsesRequest(upstreamCtx, c, account, body, token, grokCacheIdentity, s.cfg)
 	} else {
 		upstreamReq, err = s.buildUpstreamRequestOpenAIPassthrough(upstreamCtx, c, account, body, token)