Edit: I may have misread your question. Upon re-reading, I suggest downloading the version of macOS you want to boot from outside the Mac app store. This will prevent an automatic install on your own machine, but will still give you access to a file of the entire OS which you can do with as you please.
Previous comment:
Once you install a new version of macOS, that will replace the previous version you have installed. If you are wanting to download a new version to perform a single task, and then return to your computer as it now with your current version of macOS, you have a few options that require intermediate to advanced steps.
Your options include:
- Running virtualization software such as Parallels or VM Ware Fusion. This option will cost a minimum of $99, but it does not require extra hardware. You can install any version of macOS inside of Parallels and run it as if it were it's own application on your current Mac.
- You can install a new version of macOS onto an external drive, then you can boot from the hard drive instead of your MacBook's own hard drive. If your MacBook Air has an M1 or M2 chip inside, this will require you to have a high speed external hard drive or SSD in order to boot from it. This will require some deeper knowledge that you can find elsewhere on the internet.
- If you install the new macOS and wish to return to a previous version, there may be an option to downgrade. However, if you want to return to a previous version of macOS, but you may lose some data in the process.
If these options are a little over your head, I would tell your friend to find their own solution!