Is there any formal way to get s list of my account's meeting(s) that are currently on air?

Business accounts have access to the Dashboard, which does show all active meetings hosted by your account. You can read more about that feature here: https://support.zoom.us/hc/en-us/articles/360039017432-Dashboard-for-meetings-and-webinars

Hope that helps and please make sure to mark the solution as accepted if this information is what you needed.