Later you get into another whole debate about movable types and what T should be once it's moved from (for example if you want to turn that std::optional<T> into a std::shared_ptr<T>), if it only has non-trivial constructors. An idea that just popped into my head would be to have a T constructor from std:optional<T>&&, which moves from it and resets the optional. But then it's not a real move constructor. With move constructors, a lot of times you just have to accept they'll have to leave the other object in some sort of empty or invalid state.
I'm not saying it's perfect but it's better than dealing with C++ exceptions. At least with error codes you can manually do some printing to find out what went wrong. With C++ exceptions you don't even get a line number or a stack trace.
You also don’t have to make the anemic constructor public.