Startup drive is on Mac HD.
Don't know how to check or change allocation to startup.
Upgrade is direct download.
To check the space on your startup drive, select your startup drive in Finder and do a Get Info.
Deduct Used from Capacity to determine free space.
If you downloaded the installer file directly, I recommend rebooting into Safe Mode (restart and hold down the Shift key until you get to the login screen. Log in and locate the installer file. The file name should be
Install macOS Big Sur.app for Big Sur and
Install macOS Monterey.app for Monterey. Double-click to launch it and the installation should start after a “short” wait, depending on the speed of your system.
Doing the installation in Safe Mode is important because it will prevent unnecessary background processes from interfering with the installation.