How to store std::atomic in a structure as a value in std::unordered_map?

Question

The std::atomic is totally fine to be stored as a value in std::unordered_map regardless of the question "what it means to allow a copy of atomic", it even can be stored in std::pair in the value.

But when it comes to store a structure which contains std::atomic the compiler comes with hard to understand error messages.

The code

Here is the demo

#include <atomic>
#include <string>
#include <unordered_map>

struct LexemData {
    unsigned int id{};
    std::atomic<size_t> counter{};
};

std::unordered_map<std::string, std::atomic<size_t>> dict1;

std::unordered_map<std::string, std::pair<unsigned int, std::atomic<size_t>>> dict2;

std::unordered_map<std::string, LexemData> dict3;


int main()
{
    std::string lexem("lexem");
    
    dict2.insert({ lexem, std::make_pair(0, 0) });

    dict2.insert({ lexem, {0, 0} }); // This doesn't compile (1)

    dict3.insert({ lexem, LexemData {0,0} });  // This doesn't compile (2)
}

What makes both cases above so different from pure std::atomic storage and storing through std::make_pair that:

1. inserting with initialization list doesn't work
2. inserting of the structure object doesn't work

I guess the question "what it means to allow a copy of atomic" can be equally addressed to all approaches here.

What can be done to make them working?

I am especially interested in the second case, I feel that I miss some kind of operator or way to return a reference instead of object to be provided, but I can't see it.

The error messages are too verbose to be put here; if somebody knows how to do it, please edit the question so that I could learn.