MacOS Monterey 12.4 installation stuck at 2h 57 minutes. Tried safe mode, recovery mode. Still same error.

Then your two options are to perform a clean install by following the instructions in this Apple article making sure to follow the "Erase Disk" link within that article as well:

How to reinstall macOS - Apple Support

Erase Disk link:

Use Disk Utility to erase a Mac - Apple Support

If you have access to another qualifying Mac from 2013 - 2022, then you can create a bootable macOS USB installer using the instructions in this Apple article:

How to create a bootable installer for macOS - Apple Support

A "Qualifying Mac" means the host Mac being used to download the installer must also be able to run that version of macOS, although the host Mac can currently be running any version of macOS. For example you can create a bootable macOS 11.x Big Sur USB installer using most Macs from 2014 - 2020 (even a couple from late-2013), while you will generally need a Mac from 2015+ for creating a bootable macOS 12.x Monterey USB installer. See this article for which versions of macOS are compatible with various Apple hardware:

https://eshop.macsales.com/guides/Mac_OS_X_Compatibility

If that still fails, then you will need to "Restore" the system firmware (requires access to another Mac running macOS 10.15+):

Revive or restore a Mac with Apple silicon using Apple Configurator - Apple Support

If none of this works, then you will probably need to have Apple or an Apple Authorized Service Provider examine your laptop to assist you.

It helps to know the exact model of your Mac since different Macs have different issues and can behave differently. Plus some Macs require certain procedures while others do not. You can get this information by entering your serial number here:

Check Your Service and Support Coverage - Apple Support

Did you try Internet Recovery Mode using Command + Option + R (Intel Mac only)? Did you erase the whole hidden Container when performing the clean install (or the physical SSD if an Intel Mac)? Within Disk Utility you may need to click "View" and select "Show All Devices" before the hidden Container or physical SSD appears on the left pane of Disk Utility. You can only erase the physical drive on an Intel Mac. If you erase the physical drive on an M1 Mac, then you will make it unable to access the special startup modes. Another reason to always post the exact model.

If this is a 2018+ Mac, then you can "Restore" the system firmware instead (requires access to another Mac running macOS 10.15+):

Revive or restore an Intel-based Mac using Apple Configurator - Apple Support

Revive or restore a Mac with Apple silicon using Apple Configurator - Apple Support

So after performing the Restore of the firmware you were presented with Setup Assistant helping you set up the new OS?

Did you actually try creating a new user account and testing before trying to set things up? Or did you just migrate or restore from a backup? If the latter, then perhaps you brought the problem back. If you did not migrate/restore from a backup how did you set up the computer?

Is this a normal macOS login screen or another type of screen asking you to authenticate for some other reason?

Try booting into Safe Mode to see if that works any better.