fix(tools): improve web search provider fallback (#2629)

- centralize web search provider readiness and resolution logic
- fall back when the configured provider is unavailable or invalid
- allow native-search-capable models to use built-in search without the client tool
- simplify the tools page and add direct access to web search settings
- add backend, agent, and integration tests for the new selection behavior

pkg/tools/integration/web_test.go

@@ -385,24 +385,14 @@ func TestWebFetchTool_PayloadTooLarge(t *testing.T) {
 	}
 }
 
-// TestWebTool_WebSearch_NoApiKey verifies missing credentials are surfaced at execution time.
+// TestWebTool_WebSearch_NoApiKey verifies providers without required credentials are not registered.
 func TestWebTool_WebSearch_NoApiKey(t *testing.T) {
 	tool, err := NewWebSearchTool(WebSearchToolOptions{BraveEnabled: true, BraveAPIKeys: nil})
 	if err != nil {
 		t.Fatalf("Unexpected error: %v", err)
 	}
-	if tool == nil {
-		t.Fatalf("Expected tool when Brave is enabled, even without API keys")
-	}
-
-	result := tool.Execute(context.Background(), map[string]any{
-		"query": "test query",
-	})
-	if !result.IsError {
-		t.Fatalf("Expected missing Brave API key to return error")
-	}
-	if !strings.Contains(result.ForLLM, "no API key provided") {
-		t.Fatalf("Unexpected error message: %s", result.ForLLM)
+	if tool != nil {
+		t.Fatalf("Expected nil tool when only enabled provider is missing credentials")
 	}
 
 	// Also nil when nothing is enabled
@@ -1878,6 +1868,94 @@ func TestWebTool_AutoProviderPrefersConfiguredProvidersBeforeSogou(t *testing.T)
 	}
 }
 
+func TestWebTool_ExplicitProviderFallsBackWhenMissingCredentials(t *testing.T) {
+	tool, err := NewWebSearchTool(WebSearchToolOptions{
+		Provider:        "brave",
+		BraveEnabled:    true,
+		SogouEnabled:    true,
+		SogouMaxResults: 5,
+	})
+	if err != nil {
+		t.Fatalf("NewWebSearchTool() error: %v", err)
+	}
+	if _, ok := tool.provider.(*SogouSearchProvider); !ok {
+		t.Fatalf("expected SogouSearchProvider after fallback, got %T", tool.provider)
+	}
+}
+
+func TestWebTool_ExplicitProviderFallsBackWhenMissingBaseURL(t *testing.T) {
+	tool, err := NewWebSearchTool(WebSearchToolOptions{
+		Provider:        "searxng",
+		SearXNGEnabled:  true,
+		SogouEnabled:    true,
+		SogouMaxResults: 5,
+	})
+	if err != nil {
+		t.Fatalf("NewWebSearchTool() error: %v", err)
+	}
+	if _, ok := tool.provider.(*SogouSearchProvider); !ok {
+		t.Fatalf("expected SogouSearchProvider after fallback, got %T", tool.provider)
+	}
+}
+
+func TestWebTool_AutoProviderSkipsEnabledButUnreadyProviders(t *testing.T) {
+	tool, err := NewWebSearchTool(WebSearchToolOptions{
+		Provider:        "auto",
+		BraveEnabled:    true,
+		SogouEnabled:    true,
+		SogouMaxResults: 5,
+	})
+	if err != nil {
+		t.Fatalf("NewWebSearchTool() error: %v", err)
+	}
+	if _, ok := tool.provider.(*SogouSearchProvider); !ok {
+		t.Fatalf("expected SogouSearchProvider when Brave has no API key, got %T", tool.provider)
+	}
+}
+
+func TestResolveWebSearchProviderName_FallsBackFromExplicitUnavailableProvider(t *testing.T) {
+	got, err := ResolveWebSearchProviderName(WebSearchToolOptions{
+		Provider:        "brave",
+		BraveEnabled:    true,
+		SogouEnabled:    true,
+		SogouMaxResults: 5,
+	}, "")
+	if err != nil {
+		t.Fatalf("ResolveWebSearchProviderName() error: %v", err)
+	}
+	if got != "sogou" {
+		t.Fatalf("ResolveWebSearchProviderName() = %q, want sogou", got)
+	}
+}
+
+func TestWebTool_UnknownExplicitProviderFallsBackToAuto(t *testing.T) {
+	tool, err := NewWebSearchTool(WebSearchToolOptions{
+		Provider:        "totally_unknown",
+		SogouEnabled:    true,
+		SogouMaxResults: 5,
+	})
+	if err != nil {
+		t.Fatalf("NewWebSearchTool() error: %v", err)
+	}
+	if _, ok := tool.provider.(*SogouSearchProvider); !ok {
+		t.Fatalf("expected SogouSearchProvider after fallback, got %T", tool.provider)
+	}
+}
+
+func TestResolveWebSearchProviderName_FallsBackFromUnknownProvider(t *testing.T) {
+	got, err := ResolveWebSearchProviderName(WebSearchToolOptions{
+		Provider:        "totally_unknown",
+		SogouEnabled:    true,
+		SogouMaxResults: 5,
+	}, "")
+	if err != nil {
+		t.Fatalf("ResolveWebSearchProviderName() error: %v", err)
+	}
+	if got != "sogou" {
+		t.Fatalf("ResolveWebSearchProviderName() = %q, want sogou", got)
+	}
+}
+
 type stubSearchProvider struct {
 	result string
 	calls  []string