I signed a HiWi contract and now I need to tell them I can’t work there anymore. Am I screwed?

So I applied for a HiWi position around May. One of the reasons I wanted the HiWi was because, as I understood it, the HiWi hours would not count toward my 140 day work limit, so I could continue earning an income until my work rights reset.

The whole process took forever. There was an interview, then the contract preparation, and everything else. I finally signed the contract in August, and the entire team is apparently relying on me to start in September.

The problem is that a new opportunity unexpectedly came up at a really good company. I have already used most of my 140 days because of my internship, but I still have some days left. The new company said they can reduce my working days in the contract so I do not use up all my remaining days. I would start in October and somehow manage until the end of December. After that, my contract would become a normal 20 hour per week contract once my work rights reset.

Obviously, I had no idea this opportunity was going to come up when I accepted the HiWi position.
Now I have realized that I apparently cannot continue the HiWi job as well, because combining both jobs would put me over the 20 hour weekly limit. I initially thought I could do both, but apparently that is not allowed.

So now I have to tell the university that I cannot take the HiWi position after all. Honestly, I feel terrible about it. I already signed the contract, they spent time going through the whole hiring process, and they are expecting me to start in September. I feel like I am screwing them over at the last minute.
I know the new opportunity is probably the smarter career decision, especially since it is at a good company, but I am extremely stressed about how the university and the team are going to react.

Has anyone been in a similar situation? How bad is this really? Am I completely screwed for backing out after signing the contract? And is there anything I should be particularly careful about when telling them?