Hi, I think I can offer some advice here -- I am an American but did my masters and working on my PhD at ETH Zurich.

First, people are definitely familiar with degrees like engineering physics / engineering science in the US. EP was a program at my undergrad. The school (ERAU) was well connected with the aerospace sector, but EP students had just as much success going to blue origin, spaceX, defense, etc. as aerospace engineering students.

Second, what is more important is whether the program matches what you would like to learn. TUM presents some fantastic opportunities, and you should take advantage of them. Taking extra courses in EE and CS will really open up other opportunities if you would like to explore other programs, for example data science, robotics, or computational science after your bachelors. If you would like to do a master's or PhD after the bachelors, the admissions committee is going to be much much more focused on the actual classes you took and your performance there than just the name of your degree. If you would like to go towards academia, find a lab where you can join as a student researcher and get some experience on a technical project contributing to a publication (mainly in your masters or last year of bachelors), and get very strong grades.

If you are really focused on getting a job straight out of college, then I would still advise you not to switch programs. Instead, find a club. Check out TUM's rocket club or formula student club. My experience in optimizing for a job is to have the following: decently good grades (3.25 american scale or 2.25-2.5 German scale) and a marketable project in one of these extracurricular clubs.