Check in the Application folder for " Install Monterey " if it exists. Drag and Drop to Trash and Empty the Trash.
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
5 - Running behind a VPN which may increase Packet losses
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
This method may seem unnecessary but sometimes the Router Restart clears Network issues from ISP to Apple Servers
1 - Shutdown Router. Shutdown computer and disconnect all External Drives. Restart Router.
2 - Connect to Router via Ethernet Cable. If via Wifi - Disconnect all other Devices using the Wifi - want the Maximum Bandwidth only for this computer.
3 - Restart computer in Safe Mode. It does a Repair Disk, Clear System Cache files and only load Apple Software, extensions and Fonts. Will load slowly - Normal.
4 - Once Logged in - open Apple Apps Store and Get the Full Version of Monterey.
5 - It will take some time and several pauses will occur - normal. Countdown clock may say 15 minutes but in Real time may be 30 minutes.
6 - Same goes for clock at 10 minutes could be 20 minutes in Real time. Eventually , Full Installer will download and a New Application in Applications Folder will present called Install Monterey
7 - Stop there and perform a Time Machine Backup.
8 - If desired - have an External Drive - Copy & Paste the Install Monterey Application to external drive for future usage - making a Bootable Installer.
9 -Now run the Installer.