Almost always cache check/put operations are followed by returning results to the callee, e.g.

auto val = std::shared_ptr{nullptr};

const auto [cached_val, cached_ok] = cache.TryGet(key);

if (!cached_ok) {
  # for example, val is already a shared_ptr
  val = Calc(key);
  cache.Put(key, val);
  return val;
}

return cached_val;

so current implentation doesn't allow storing shared_ptr, only shared_ptr<shared_ptr>.

Otherwise we must always copy the object to the cache because Put doesn't return a shared_ptr for newly created smart pointer, if it did, we could have done

const auto [cached_val, cached_ok] = cache.TryGet(key);

auto val = SomeType{};

if (!cached_ok) {
  val = Calc(key);
  auto val_shared_ptr = cache.Put(key, std::move(val));
  return val_shared_ptr;
}

return cached_val;

although, looking again at the code, even with a move in the latter case, Insert will anyways initiate a copy constructor, which does not seem right for large objects