How to implement a singleton provider for qmlRegisterSingletonType?

it just feels wrong to write a singleton provider which returns a new instance when called from different cpp files. So I tried an own implementation where I use a static class member to return the instance

Quote from documentation to qmlRegisterSingletonType function:

NOTE: A QObject singleton type instance returned from a singleton type provider is owned by the QML engine. For this reason, the singleton type provider function should not be implemented as a singleton factory.

It means that such behaviour when singleton type provider returns a new instance is done by intention despite the fact that it, as you have noted, looks weird at first glance. So, your class implementation should look something like below:

class MySingleton: public QObject
{
    Q_OBJECT
    Q_DISABLE_COPY(MySingleton)

    MySingleton() {}

public:
    static QObject *qmlInstance(QQmlEngine *engine, QJSEngine *scriptEngine)
    {
        Q_UNUSED(engine);
        Q_UNUSED(scriptEngine);

        return new MySingleton;
    }
};

Moreover, you should use ampersand for MySingleton::qmlInstance since it is a member method. See this for more info. Then registration should look so:

qmlRegisterSingletonType<MySingleton>(uri, 1, 0, "MySingleton", &MySingleton::qmlInstance);