How can I respond to a repair request if I’m locked out of my Apple account?

I recently sent my iPhone 15 for repairs, but now I'm facing a big problem. While I was signed in on my laptop, it seems I got logged out, and the password I have doesn't work. I'm completely locked out of my Apple account, and I can't access my original device either since I don't have the phone number connected or any other way to get in. I tried to reset the password, but it'll take several days. My phone has been inspected, and I need to provide instructions on how to proceed within the next few days. However, I can't find any way to respond since I can't access my account, and there's no number to call. I'm feeling pretty stuck here. Is there a workaround anyone knows about?