Welcome to the Wefugee Community!
Are you holding a so-called "Permesso di soggiorno CE per soggiornanti di lungo periodo" in Italy? If yes, I found some relevant information on the website of the German Embassy in Italy. The following document (https://italien.diplo.de/blob/1457226/f454316b8e60d097365623ad537a0b0d/visa-daueraufenthalt-eg-data.pdf ) states, that you usually do not need a visa for Germany, even if you stay longer than 90 days. However, if you want to work, you need to contact the local "Ausländerbehörde" (immigration office) after you arrived to apply for a residence permit. The residence permit would allow you to work.
If the Ausländerbehörde has not issued a residence permit after 90 days, you need to leave the country again and apply for a visa.
I hope this information will be useful and please get back to us with any further questions.
All the best,