I have a MacBook Air (Reina 13-in, 2018) MacOS Big Sur 11.6.2. I have a notice to install Monterey 12.2.1. Is this compatible?

Suggestion - so people have attempting the upGrade to Monterey with a Not 100% Updated version of Big Sur.Some have had success and others have not.

Conservative approach would to update Big Sur to current version 11.6.4 First.

Then attempting the Monterey upGrade.

Do you have a Rescue Plan In-Place. This comprises having 3 Backups using 2 methods and 1 Off Site incase of Theft, Loss or Natural Disasters. A Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS. 

For addition purposes - two Tested Bootable Clones each to separate external drives. This is insurance incase the upgrades goes sideways. At least one Tested Clone and / or Time Machine Backup should be Off - Site

Yes.

In addition to what has been said - make sure that you:

1) Have a solid backup

2) Have enough free space available on the system drive - probably 45GB or more.

You're welcome.