What do you think about introducing a new base class for servers? One based on what is actually useful. It would be more a guide than a useful base class, but for Client and UDP the base classes do an excellent job for consistency of the networking API implementations.

template <class TClient>
class ServerNew {
 virtual void begin(uint16_t port) = 0;
 virtual void end() = 0;
 virtual explicit operator bool() = 0;
 virtual TClient accept() = 0;
};
#define CORE_HAS_SERVERNEW

It doesn't require the confusing available method and the never used print-to-all-clients' functionality.
It has parameter port for begin, it doesn't have to be in constructor.

The library authors could ifdef their server class declaration.

class EthernetServer 
#ifdef CORE_HAS_SERVERNEW
 : public ServerNew<EthernetClient>
#endif
{

or even

class EthernetServer :
#ifdef CORE_HAS_SERVERNEW
 public ServerNew<EthernetClient>,
#endif
 public Server
{

would work

Here is an overview of Server implementation in libraries
https://github.com/JAndrassy/Arduino-Networking-API/blob/main/ArduinoNetAPILibs.md#server-class