Software update on my MacBook Air has failed and I can't get any further?

Hi.

I finally wanted to do a software update on my MacBook. To do this, I cleared a bit of storage space and started the update. At first everything went well and there was I would have to wait another 28 minutes. I did and then the message came that you can see in the photo. I've now figured out that the problem was likely that there wasn't enough memory after all. Now the whole thing has kind of hung up. If I click ok on the message, the one you see in the second picture will appear. Since I can somehow only click on hard drive mofus. If I click up there, then it comes back that I should wait 28 minutes and then it starts all over again with the messages. So my laptop somehow got stuck in this installer.
Can someone help me somehow? The update doesn't even have to be installed successfully, I could do without it for now, but I just need access to my laptop again because I'll be writing an exam in 2 days and all my summaries are on it. I'm about to have a crisis 😂

Would delete all data and reinstall macOS (CMD + R) I think