I have moved to Germany as an EU (British) citizen, and completed the standard Anmeldung upon arrival. I work remotely for an Italian employer. Are there any further bureaucratic processes to go through as an EU citizen1 who plans to remain in Germany indefinitely? For instance in Austria, in addition to my Anmeldung, I had to get an Anmeldebescheinigung (requiring proof of employment, etc.), in order to stay for longer than three months. Does Germany have something similar, or is the Anmeldung truly the only formality required for EU citizens?
Incidentally, I asked about this at my local Meldeamt and was told verbally that the Anmeldung really is sufficient. However, the staff member who told me this seemed a little confused about the situation, and was clearly in a hurry to get through with me and on to the next person in the enormous queue at the counter. In any case, I think a firm written answer to this question would be useful for others in a similar situation.
1I realize that in my own case, Brexit may complicate things in the long run, but please ignore that factor for the purposes of this question.