I do not know how things are with covid in these countries now, but I think that you do not need to take any tests with you or fill them out. Although before you would fly to Germany, I will clarify this information. Although I literally flew to Austria a month ago and there were no problems, I didn't even have to fill out any documents about covid, etc. And by the way, since you are flying to Germany, I advise you to travel around Austria, especially since trains run regularly from Germany to Austria. By the way, I advise you to look at the exact train schedule on this site -- https://www.oebbfahrplan.com/de/.
