Yes, this is the correct way. Importing only creates a copy. It will not keep the two in sync automatically.
The limiting factor is always how much time you have to spend on it. One possibility is to set up a repo on a machine you control where you can do a git fetch and git push each branch
The problem is Some teams have access to GitHub and other teams have access to Azure Git. As you said, for development activities, we can use Azure Git and for showcase purposes (to other teams),
we can push the changes to GitHub periodically. Thanks!