hi, i had same issue.
after a day searching, debug and tracing finally i have it done.
as you say the issue was Websocket module wasn’t loaded. so by using ModuleManager and load it on runtime made it work.
#include "Modules/ModuleManager.h"
if(!FModuleManager::Get().IsModuleLoaded("WebSockets"))
{
FModuleManager::Get().LoadModule("WebSockets");
WebSocket = &FWebSocketsModule::Get();
}