How can I recover my data? I contacted Apple to solve an issue, and now I’m facing an even bigger problem.

I think you are beyond the point of salvaging any data from this computer now that the erase process has started.

FYI, what the Apple tech was trying to tell you was to turn off FindMy for your laptop by logging into the iCloud website....not actually removing the whole device from iCloud. If you are unable to boot the laptop where you can easily turn off FindMy in the AppleID section of System Settings, then you would need to log into the iCloud website and remove the device from FindMy......not remove it from iCloud itself. Here are the two Apple articles which explain the procedure:

If you can still log into the device to be repaired:

Turn off Find My on your devices and items - Apple Support

If you cannot log into the device being repaired (this link came from within the previous article):

Remove a device from Find Devices on iCloud.com - Apple Support

Unfortunately some of Apple's products & features are confusing & poorly documented including the information presented in dialog boxes when accessing & configuring them. I know turning off FindMy when the device is non-functioning can be very confusing & difficult to do because I have personally tried to assist co-workers in this endeavor with mixed results.....sometimes we have been unable to even see the device, nor has it always been successful. It is not always as simple as Apple makes it out to be.

anagsoares wrote:

My new MacBook Air is experiencing a series of issues. When I spoke with an Apple representative, they suggested that I send the MacBook in for repair via courier. However, they asked me to remove the Mac from iCloud. After doing this, I received a message by email:

"All data will be permanently erased. This process may take several hours, depending on the Mac model and the size of the hard drive."

And my MacBook restarted from scratch, asking to install macOS Sonoma.

However, I need to make a backup before sending it by mail. At no point was I warned that the data would be erased.

How can I recover it now? This is urgent.

https://discussions.apple.com/content/attachment/a26213ab-e7a8-411e-bf3e-062ffcddcbed

I contacted Apple to solve an issue, and now I’m facing an even bigger problem. I don’t save my data in iCloud.

I think there may have been some miscommunications or misunderstands somewhere between the two principal persons

I can not say for sure as I was not privy to the conversation

Judging from this "All data will be permanently erased. This process may take several hours, depending on the Mac model and the size of the hard drive."

And my MacBook restarted from scratch, asking to install macOS Sonoma."

It seems this was suggested >> Erase your Mac and reset it to factory settings <<

If so, the comments from my learned colleague @BobTheFisherman would come into play / important

Without some type of backup done Before the erasure was done, the data is gone and can not be retrieved

If you have used or are using Time Machine Backup Utility  you maybe able to Restore the Deleted Files 

For future purposes

To truly protect your non replaceable Data - have a 3-2-1 Rescue Plan in place and always current

3 Backups using 2 methods and 1 off site incase of natural disaster or un-natural disaster.

Each of the above should be done to a Dedicated Single Purposed External Drive 

https://bombich.com

Your data should be on your backup drive. I assume you have a Time Machine or other backup of your data.

Op wrote " Witch code?! "

How to check the Status of Repairs

My Support - Official Apple Support