Hi @DR838429, great question. We don't use Azure but we do use a combination of Team Foundation Server as a build and release server against repos in GitHub and Git within TFS. Almost all of these uses are by App Dev teams and not by the data warehouse team. It sounds like you are trying to use your own method of Git implementation without going to the larger instance that includes the Git Integration. Is that correct? This isn't a bad thing by the way nor is it frowned upon in my opinion.
The problem with exporting a project in Matillion is that you only get the project. It doesn't sound like a problem until you want to include things like the Passwords in the Password Manager or the Shared Jobs which are dependencies in projects if you are using them. What I am getting at is that in most cases, just the project export is not enough. The other issue I have seen is that Matillion can add, remove, or change their JSON schema for exports depending on the version of Matillion you are using. Meaning, if you fast forward a year, you will likely be on a new version of Matillion and the old version of the project in Git may no longer work in the current version of Matillion. If they do work they likely will not work the same as they did when the project was pushed to the Git repo.
You may look at my post from yesterday about deployment from one instance to another (https://matillioncommunity.discourse.group/t/do-you-have-a-need-to-control-your-deployments-from-one-instance-to-another/1214). This still doesn't solve all the issues I posed above but it does get closer in that it would include all the dependencies. You could theoretically use Azure DevOps to execute a Python script that would do the export to files for the project group, project, shared jobs, API profiles, etc. then push those to the Git Repo. You could likely just take the export Python script and modify that one file and get everything you need.
I have had some conversations with Matillion about this topic and it's definitely something they are looking to improve upon. It's just something they don't have yet.
I hope this helps in some form or fashion. Let us know if you come up with an awesome way of doing this outside of the approach I threw out there. Thank you!