macbook stuck on preparing to restore macintosh screen

I had the exactly same issue as you faced. When I contacted the Apple customer service to ask about this issue, the rep. said I need to wait until the whole process finishes. Thus, I waited for several hours, but I could not see any change on the screen at all. I felt something is wrong since "preparing to restore" doesn't mean the actual restoring process. After several tests, I successfully restored my previous backup from my external SSD having Time Machine full backups. I would like to share my experience.

My case:

My device is MacBook Pro 16inch 2019 (Installed OS: Catalina). I upgraded macOS from Catalina to Monterey for the Logic 10.7. However, the Logic 10.7 has sluggish loading issues and I decided to go back to Catalina again with my time machine full backup.

When I tried to restore my backup, the macOS recovery initially showed an error that the backup could not be restored into the main SSD and thus I exited the restoration process and ran it again without rebooting. After selecting the restoration target drive, the restore button didn't work at all. So I did rebooting and I could see the restore button and run it. Unfortunately, it was stuck on preparing to restore Macintosh HD... for several hours.

Problem:

I think this issue comes from a version conflict between the macOS recovery firmware pre-installed when the MBP was shipped and the backup data. When you enter the macOS recovery, if you cannot see the 2D rotating earth globe with the title "internet recovery", it may be a pre-installed recovery firmware. This firmware doesn't allow you to install the original OS version. I could see Monterey reinstallation option, not the original Catalina reinstallation.

Solution:

What you need before these steps:

• your external time machine backup drive (should be connected to the MBP before entering the recovery firmware)
• the internet connection.

1. Erase the main Macintosh HD in your main SSD. In the macOS recovery, select the Disk Utility and erase the main Macintosh HD. Then exit the disk utility and turn off your MBP. Don't be afraid, you will be fine. This step will erase the pre-installed recovery firmware.
2. Turn on your MBP while pressing cmd+r until the apple logo pops up.
3. Now you can see the internet recovery with the 2D rotating earth globe (I had never seen this before erasing the main drive). Select your WiFi router and make the internet connection. It requires apple login with your Apple ID and PWD for authentication. Then it will automatically download the new recovery firmware. There is a progress bar under the logo, but it doesn't show the actual size and takes several minutes. In the middle of downloading, if you face an error like me, don't worry. Just reboot it and it will automatically continue the downloading after the end of previous downloading.
4. After success of automatic downloading, you will see the macOS recovery options with slightly different design. Now you can reinstall the your original OS (my case is Catalina, not Monterey). Select the restoration option and select the backup source drive and the target drive and finally press the restore button. The step of "preparing to restore Macintosh HD..." takes only several minutes and then it starts the actual restoring process showing restoring data size and estimated time. Less than 1 hour, my full backup restoration (~300GB) was done!

I hope you can restore your backup soon. Good luck!

Shame on you, Apple customer service! You guys should provide the solution for this issue, not by customers!