Is inDesign version 15.x compatible with macOS Monterey?

Yes it should run, though the official release notes state that the latest OS that will run version 15.x is Catalina. See the following link for details

https://helpx.adobe.com/indesign/system-requirements/2020.html

So the question now arises as to why do you want an older version when your machine is capable of running the latest version. In addition Adobe supports only the latest 2 versions, that would be version 17 and 16. So if you have the installer give it a try and hopefully you can run it, else you don't have an option other than using the supported versions.

-Manan