Startup Disk

To perform this action will require booting from a Bootable Installer. 

This will have to be performed from a Qualifying Computer to run the version of macOS to be made on the Bootable Installer.

Only as Example : Bootable Installer of Big Sur would have to be done on a computer that Qualifies to run Big Sur.

Notation: If the computer being used to perform this action is Too New or Too Old to qualify to run the version of macOS - this computer can not be used.

The only alternative is to get access to an Apple Computer that qualifies to run the version of macOS one whats to put on the USB Installer Drive

if your mac is compatible with monterey, then yes it can be done. but there is a catch. when installing monterey, there is a required firmware update for the mac that checks for an OEM Apple SSD / HDD. to be able to install monterey on the external SSD, it appears as though the host computer must first be upgraded to monterey BEFORE you install monterey on the external drive.

also, there have been reports of some users attempting to upgrade from catalina directly to monterey running into issues with the install. i would highly recommend first upgrading to big sur, and then on to monterey.

once those conditions have been met, you can read this well written and very informative user tip to install monterey onto the external drive: How to Setup and Use an External SSD as your Startup Disk - User Tip

actually, i think i misunderstood your question. if you want to create a catalina boot drive work with your MBA (monterey) the MBA needs to have been delivered with no later than catalina installed. if the MBA shipped with big sur or monterey, you cannot use it to run catalina from the external drive.