Welcome to the Wefugees Community and thank you for reaching out to us. First of all, congratulations!
Having the EU-citizenship will most probably make things easier for you and your family and you enjoy the so-called "freedom of movement" within the European Union now. I have to say that it's rather unusual that someone granted an EU-citizenship during an asylum procedure. Therefore, I can not share much of experience how authorities in Germany deal with it. I highly recommend you to get support in a migration counselling office now to manage the necessary steps well and to communicate with the involved authorities. I believe that you should withdraw your asylum application now since it will be rejected for people who come from safe countries (incl. the EU). As an EU-citizen, you are allowed to work in Germany without any restriction. EU-cititzens are entitled to receive jobcenter allowances if they are employees. So if you work in a Minijob, for instance, and don't earn enough to cover your family's cost of living, you can receive additional unemployment benefits. If you are currently living in a refugee accomodation, they will most probably ask you to move out. But as an EU-citizen, you are not obliged to live in a certain municipality or federal state. You may live wherever you find housing, work etc.
I hope this helps in the first place and don't hesitate to keep us updated or get back to us with any further questions. In any case, I highly recommend to get individual legal advice - we can only give general answers here on this platform.
All the best,