what is the latest version of iOS I can install on a Macbook Air Model A1369 (mid 2011)?

Your 2011 mac can only upgrade as far as macOS High Sierra.

Please use Safari to access the following link do not use Firefox

How to upgrade to macOS High Sierra - Apple Support

Before upgrading make a full back up of your Mac.

Check that third party apps you use have updates available for the new OS.

https://roaringapps.com

Check that your printers/ scanners etc have updated drivers and software available for the new OS.

Connect your mac to your router via cable rather than rely on WiFi.

Do not use your mac while it is downloading

and do not use any other devices that share the same internet connection.

If the App Store says ‘Open’ then it is detecting a previous download of the install app

go to the Applications folder locate Install macOS High Sierra.app.

Move it to the Trash, empty the Trash.

Restart, click on the link again, the App Store should say ‘Get' or 'Download'.

It won't run any version of iOS. iOS is a mobile device OS.

You can check which OSx works here: https://everymac.com/systems/by_capability/maximum-macos-supported.html