C++ Compile time check for existence of functions matching enum keys

In the project I'm working on we have a large number of classes with methods named to match enum keys. This provides a means to call functions that can be dynamically detected.

General example of these classes:

template <class ImplType>
class BaseTemplate
{
...
};

class A : public BaseTemplate<A>
{
public:
  enum class Methods : int
  {
     DoAThing,
     SecondItem,
     ItemNumberThree,
     FinalAction
  };

private: 
  void doAThing();
  void secondItem();
  void itemNumberThree();
  void finalAction();
};

The methods are called by another mechanism (more on this below). I'd like a means to have a compile-time check that the method names match the keys in the enum, so to have a compiler error if a key in the enum is not matched by a function.

Notes:

• The classes inherit a base class with other business functionality (not shown). Since this is using CRTP to capture the type of the derived object, we would ideally add checks there.
• I can use C++20 and potentially C++23, so consteval and similar features are available.
• As in the example, enum keys must be CapitalCamelCase, methods named lowerCamelCase. The only difference is the case of the first letter.
• This is a Qt project -- the enum here is a Q_ENUM and the methods are private Q_SLOT. I've not put these in the example, as if possible I'd prefer a pure C++ solution.
  In the actual application, we use meta-object reflection to enumerate the enum keys, and so to achieve calls to the possible methods. However, I suspect the Qt metaobject system is unlikely to be useful for compile-time checks. We already have run-time assertions on missing methods. If Qt can somehow be used for this, perhaps after the Moc compile step, that would be acceptable.