[Extensions] Expand bindings access checks

BUG=601149
BUG=601073

Review URL: https://codereview.chromium.org/1866103002

Cr-Commit-Position: refs/heads/master@{#387710}
void ObjectBackedNativeHandler::SetPrivate(v8::Local<v8::Object> obj,
                                           const char* key,
                                           v8::Local<v8::Value> value) {
  SetPrivate(context_->v8_context(), obj, key, value);
}

void ObjectBackedNativeHandler::SetPrivate(v8::Local<v8::Object> obj,
                                           const char* key,
                                           v8::Local<v8::Value> value) {
  SetPrivate(context_->v8_context(), obj, key, value);
}
