The transfer you originally made from the MacBook Air to the iMac does not, by itself, keep the two Macs synchronized.
Migration Assistant transfers your files, apps, accounts, and settings; ongoing synchronization is handled separately by services such as iCloud Drive or other cloud-storage services. Apple: Migration Assistant
First, make sure the files you want to keep are on the iMac. Then, on the MacBook Air, go to Apple menu >> System Settings >> [your name] >> iCloud >> Drive.
If Desktop & Documents Folders is turned on, turn it off.
Apple says that your existing Desktop and Documents files remain in iCloud Drive, while new, empty Desktop and Documents folders are created locally on the Mac. Apple: Turn off Desktop & Documents Folders
If you want the MacBook Air to stop using iCloud Drive altogether, turn off Sync this Mac under iCloud Drive.
If macOS gives you the option to keep a copy of the iCloud Drive files on the Mac, Apple places that copy in an iCloud Drive (Archive) folder in your home folder. Apple: Turn off Desktop & Documents Folders
At this point, you can use the MacBook Air's local Desktop and Documents folders for your work.
Do not delete files from iCloud Drive just to remove them from the MacBook Air, because deleting an iCloud Drive file can also remove it from the iMac and other devices using the same iCloud Drive. Apple: Delete files from iCloud Drive
If you also want the MacBook Air to stop synchronizing other iCloud information, such as Photos, Notes, Contacts, or other iCloud services, those settings need to be handled separately under System Settings >> [your name] >> iCloud.
Turning off iCloud Drive does not automatically turn off those other services. Apple: Use iCloud on your Mac
Finally, if you use another service such as OneDrive, Dropbox, or Google Drive to synchronize files, that service will need to be disconnected separately.
User level: Level 1 (4 points)
