Proposed resolution:

This wording is relative to N4971.

1. Modify [expected.bad.void] as indicated:

   namespace std {
     template<>
     class bad_expected_access<void> : public exception {
     protected:
       bad_expected_access() noexcept;
       bad_expected_access(const bad_expected_access&) noexcept;
       bad_expected_access(bad_expected_access&&) noexcept;
       bad_expected_access& operator=(const bad_expected_access&) noexcept;
       bad_expected_access& operator=(bad_expected_access&&) noexcept;
       ~bad_expected_access();
     public:
       const char* what() const noexcept override;
     };
   }
   

[ Tokyo 2024-03-23; Status changed: Voting → WP. ]

[ 2024-03-12; Reflector poll ]

Set status to Tentatively Ready after five votes in favour during reflector poll.

According to [exception]/2:

Each standard library class T that derives from class exception has the following publicly accessible member functions, each of them having a non-throwing exception specification (14.5):

1. (2.1) — default constructor (unless the class synopsis shows other constructors)

2. (2.2) — copy constructor

3. (2.3) — copy assignment operator

For good reasons, bad_expected_access<void> overrules from this general rule by protecting its special member functions. However, there's no reason these functions should not be noexcept.