Keep Claude builtin helpers aligned with the shared helper layout

The review asked for the builtin tool registry helper to live with the rest
of executor support utilities. This moves the registry code into the helps
package, exports the minimal surface executor needs, and keeps behavior tests
with the executor while leaving registry-focused checks with the helper.

Constraint: Requested layout keeps executor helper utilities centralized under internal/runtime/executor/helps
Rejected: Keep the files in executor and reply with rationale | conflicts with requested package organization
Confidence: high
Scope-risk: narrow
Reversibility: clean
Directive: Keep executor behavior tests near applyClaudeToolPrefix and keep pure registry tests in helps
Tested: go test ./internal/runtime/executor/helps ./internal/runtime/executor -run 'Claude|Builtin|Tool'; go test ./test/...; go test ./...
Not-tested: End-to-end Claude Code direct-connect/session runtime behavior

internal/runtime/executor/helps/claude_builtin_tools.go

@@ -0,0 +1,38 @@
+package helps
+
+import "github.com/tidwall/gjson"
+
+var defaultClaudeBuiltinToolNames = []string{
+	"web_search",
+	"code_execution",
+	"text_editor",
+	"computer",
+}
+
+func newClaudeBuiltinToolRegistry() map[string]bool {
+	registry := make(map[string]bool, len(defaultClaudeBuiltinToolNames))
+	for _, name := range defaultClaudeBuiltinToolNames {
+		registry[name] = true
+	}
+	return registry
+}
+
+func AugmentClaudeBuiltinToolRegistry(body []byte, registry map[string]bool) map[string]bool {
+	if registry == nil {
+		registry = newClaudeBuiltinToolRegistry()
+	}
+	tools := gjson.GetBytes(body, "tools")
+	if !tools.Exists() || !tools.IsArray() {
+		return registry
+	}
+	tools.ForEach(func(_, tool gjson.Result) bool {
+		if tool.Get("type").String() == "" {
+			return true
+		}
+		if name := tool.Get("name").String(); name != "" {
+			registry[name] = true
+		}
+		return true
+	})
+	return registry
+}

internal/runtime/executor/helps/claude_builtin_tools_test.go

@@ -0,0 +1,32 @@
+package helps
+
+import "testing"
+
+func TestClaudeBuiltinToolRegistry_DefaultSeedFallback(t *testing.T) {
+	registry := AugmentClaudeBuiltinToolRegistry(nil, nil)
+	for _, name := range defaultClaudeBuiltinToolNames {
+		if !registry[name] {
+			t.Fatalf("default builtin %q missing from fallback registry", name)
+		}
+	}
+}
+
+func TestClaudeBuiltinToolRegistry_AugmentsTypedBuiltinsFromBody(t *testing.T) {
+	registry := AugmentClaudeBuiltinToolRegistry([]byte(`{
+		"tools": [
+			{"type": "web_search_20250305", "name": "web_search"},
+			{"type": "custom_builtin_20250401", "name": "special_builtin"},
+			{"name": "Read"}
+		]
+	}`), nil)
+
+	if !registry["web_search"] {
+		t.Fatal("expected default typed builtin web_search in registry")
+	}
+	if !registry["special_builtin"] {
+		t.Fatal("expected typed builtin from body to be added to registry")
+	}
+	if registry["Read"] {
+		t.Fatal("expected untyped custom tool to stay out of builtin registry")
+	}
+}