Welcome to the Wefugees Community and thank you for reaching out to us.
Very similar questions were asked on this platform already. You may want to check this thread, for instance, for more information. Here, @mbeon-Christine was explaining that only the "Carta di soggiorno per stranieri - o tempo indeterminato" with the addition "soggiornante di lungo periodo - CE" can be a foundation for a residence permit according to §38a of the German Residence Act. However, this type of residence does not inculde a work permit automatically, but requires a concrete job offer, the confirmation of the German authorities (Agentur für Arbeit) and some other criteria (covering living costs, health insurance etc.).
I will link @mbeon-Christine here as well, maybe she can give some information regarding your family and their possibilities to join you in Germany.
All the best,