How can I run Microsoft Project on my Mac air (using IOS) only

While there's no version Microsoft Project for macOS, there are options to run something similar in the Mac.

• How to Run Microsoft Project on Mac - projectmanager

https://www.projectmanager.com/blog/microsoft-project-for-mac-how-to

• Run Microsoft Project on Mac - Parallels Blog

https://www.parallels.com/blogs/how-to-run-microsoft-project-on-mac/

{..Apple® users can use a Windows virtual machine (VM) to run Microsoft Project on Mac®..}

• MS Project Alternative for Mac and iPad - A Quick Guide

https://www.projectwizards.net/en/blog/2018/01/msprojectformac

(as there are no versions for Apple iOS ~ this is as close as either one gets)

You are welcome!

I'm glad to offer some ideas on the topic.