But I never really studied software engineering or anything related, only Electric Engineering.
But nobody in the government knows that. I don't have my diploma papers with me and have no time or interest in going to my country of origin and ask my university for it.
With a degree in computer science you are also allowed to call yourself an engineer in Germany, for anyone reading this and wondering.
As for formal education - I've seen dozens of people with an engineering diploma who barely can write a FizzBuzz, so it is not the best indicator and mostly people don't look at it when it comes to recruitment aside from big corps. Although that kinda changed lately as junior positions started evaporating and without experience the diploma is the main thing they check.
Now, there are several types of taxes you pay in Germany based on your income. One of them is the income tax, the other is called Gewerbesteuer (maybe best translated as "commmercial tax) - and the Gewerbesteuer can be significant (something like 12% of your income). Many freelancers are exempt from the Gewerbesteuer, and so are software engineers. However, I learned that you only qualify as a software engineer if you have actually studied software engineering or a closely related field. I had studied business administration. I tried to explain to them that I have been working as a software developer for over 10 years, literally doing the same job as somebody who had studied software engineering - to no avail. They woulnd't exempt me from the Gewerbesteuer.
I'm not claiming that I'm an "engineer" or that my computer science fundamentals are as good as somebody who studied computer science, but the tax exemption shouldn't be on some bureaucratic difference like what you studied a decade ago, rather on what kind of job you're doing.
Welcome to Germany!