I can't reinstall a m1 Macbook air

If your laptop is compatible with Big Sur, then use your brother's Mac to create a bootable macOS 11.x Big Sur USB installer. Once you have Big Sur installed, then you can upgrade to a later version of macOS (must be the same or later version so you can restore from the TM backup).

Create a bootable installer for macOS - Apple Support

FYI, when booting into the new Big Sur OS, make sure to use a different macOS user name so it won't conflict when you later restore from the TM backup. Plus don't worry about using your AppleID. Just do a basic setup so that you can upgrade macOS to the version you were using before you erased the laptop.

Once you get the same version of macOS installed as your TM backup, then you can restore from the TM backup.

If you did erase the entire internal SSD, then the only way to fix the laptop is by performing a DFU firmware Restore. Unfortunately that does require a Mac running a newer version of macOS. If you already have access to Apple Configurator v2.16 (available before Oct. 2023), then you just need a Mac running macOS 12.x Monterey, otherwise you need a Mac running macOS 14.x Sonoma since Apple increased the system requirements for this app (v2.17 at least according to the information in the App Store) because why not inconvenience everyone for performing a necessary task to fix your expensive device.

If you don't know anyone with such a Mac (friend, family, co-worker, school mate), then you will need to take the laptop to an Apple Store or an Apple Authorized Service Provider for assistance as @sberman previously suggested.

You can always provide Apple with product feedback here (Apple won't respond & it won't help you at this time):

Product Feedback - Apple

Seek assistance at an Apple Store or Authorized Apple Service Center.

Unfortunately, you apparently didn’t follow the instructions on how to do that properly…

Erase your Mac and reset it to factory settings - Apple Support

Make an appointment at the Genius Bar of your local Apple Store.

petkov2005 wrote:

https://support.apple.com/en-us/102506

I followed these instructions.

And what did Apple Support tell you when you contacted them as those instructions suggest?

Unfortunately, you followed the wrong instructions...

Make an appointment at the Genius Bar.