How much space is necessary to download Monterey for a 2015 Macbook Air?

Point # 3 - Empty Space Requirements  >> If upgrading from macOS Sierra or later, your Mac needs 26GB of available storage to upgrade. If upgrading from an earlier release, your Mac needs up to 44GB of available storage. 

Point # 4 - Empty Space afterwards - it is suggested to keep at least 15% of the Drive Total Capacity as Empty Space for good operations of the computer and for additional updates to Monterey to download, expand and install. If the drive is 128 GB Capacity 15% X 128 GB = 19.2 GB of Empty Space

• >= macOS Sierra, then 26 GB of available storage
• < macOS Sierra, then 46 GB of available storage

See macOS Monterey is compatible with these computers for those storage numbers. Apple has revised the lower number down from Big Sur's 35.5 GB.

The uncompressed Monterey installer is 12.4GB, and only supports 64-bit applications, printer, and scanner drivers that are specifically stated to be compatible with it. Check with your respective third-party vendors for that compatibility before you pull the trigger. Perform a last Time Machine backup of the current operating system and do not reuse that drive for the first Monterey backup, as it is your fallback strategy.

Tips Monterey Upgrade 

macOS Monterey takes up roughly 13GB in my experience so give yourself at least 15GB of room just to be safe

See the link in my other post in this thread for the official Apple available storage numbers. It is not 15GB.