To publish a version of Azure Data Studio with open-source binaries would fall under copy/modification rules, which are explicitly allowed in the license:
> Microsoft Corporation ("Microsoft") grants you a nonexclusive, perpetual,
royalty-free right to use, copy, and modify the software code provided by us
("Software Code").
> You may not sublicense the Software Code or any use of it
https://github.com/microsoft/azuredatastudio/blob/main/LICEN...