MacOs Monterey is calculating for the download but gets stuck just before the end of the bar

There are factors:

1 - Like poor Wifi connection

2 - Slow wifi connection

3 - Too many other people downloading at the same time and Apple Severs are overloaded

4 - Software on the computer interfering with the download process including AntiVirus Software

Notation: Disabling the AV Software may or may not solve the issue. Removal of the AV Software may increase the chances of the download to perform as expected.

5 - Running behind a VPN which may increase Packet losses or corruption of the download 

6 - If via wifi too many Other devices using the wifi at the same time reducing the Bandwidth to your computer. 

7 - Best Results are via Ethernet Cable to Router

8 - Restart in Safe Mode. This will perform a Disk Repair, clear cache files and only load Apple Software, extensions and fonts. The boot up will be slow and can take some time - Normal.

And try again while in Safe Mode

It would appear from your description - you have booted in Recovery Mode ( two key combination ) Command r.

Since the Monterey has not been successfully downloaded and installed - this behaviour would be normal.

It, Recovery Mode, will attempt to reinstall from the Recovery Volume associated with the drive, which is El Capitan

While still in Recovery Mode - use the Top Menu and look for Disk Utilities and run the Repair Disk Function and run it until no more error appear

When you reboot hold the OPTION key and choose your Startup disk

Sorry you are experiencing so many issues but this seems to me, it will require an On-Hands Touch to put things right.

Apple Authorized Service Provider and / or Visit a Genius at an Apple Store

You are welcome and thank you too for the update

Do come back to the Apple Support Communities ( ASC )  in the future, if / or when additional questions may arise

Keep us posted on the progress - time permitting

Welcome 🇨🇦 and only wish we could do more but working Remotely from all around the world does have its' limitations.

Turn off the computer by any means including the Power Button