Using MacBook Pro 2012 as second monitor for iMac 2021

No, not really.

The MacBook Pro is a purpose-built computing device that happens to have a captive internal display. It does NOT have any general-purpose input that can accept the astonishingly fast and unforgiving data rates required for real-time video capture and display.

A TV set or Monitor is a purpose-built device whose sole purpose is to do that job. They have gotten surprisingly affordable.

The workaround I sometimes use is File Sharing (select the correct OS at the top):

Set up file sharing on Mac - Apple Support

The Settings pane for Sharing will give instructions for connecting. Strings like <smb://mycomputer...> can be used in Safari. Since I just share files with myself, I set my user folder to share but you can share whatever you want.

It's not as convenient as a second screen, but you have two screens to work on files from your iMac Pro. You could set up Screen Sharing, but that just mirrors your screen and doesn't give any extra space.

That would be screen sharing, as I mentioned. With file sharing, you can open and work on different files on the two different computers, even though all the files are located on one computer. As munjafoot said, it's about the same as working with Google Drive (or Dropbox, or iCloud, etc.) from two computers. The only advantage to file sharing would be if it saves you from having to upload things.

That is certainly a way to connect it, but that duplicates an existing screen in a window on the MacBook. the request was for a second screen, and I presumed they meant a UNIQUE second screen.