> How would you do that without making the visitor cases explicit?

See my edit.

    std::visit([](auto &&val) { 
        std::cout << typeIdxToString[typeid(val)] << val; 
    }, var);

> E.g. you would want the '+' operator to do different things for strings and numbers.

Then overload the '+' operator, no need to put all that in the visitor lambda.