As of 3.7.0 the Hangfire fault has been fixed and i am now able to connect using passwordless authentication.
There were a few manual steps I had to take to set this up in azure using an Azure Container Instance, Managed User ID and SQL Database:
Following database creation, run the following query on the database.
CREATE USER [manageduser] FROM EXTERNAL PROVIDER;
ALTER ROLE db_owner ADD MEMBER [manageduser];
Finally, I had to swap out my connection string in my environment variables
Server=tcp:servername.database.windows.net,1433;Initial Catalog=databasename; Authentication=Active Directory Default;
Following these changes, Hangfire loaded up.
[11:29:56 INF] Start installing Hangfire SQL objects...
[11:29:56 INF] Hangfire SQL objects installed.
Special thanks to @adam for making the needed changes to Hangfire.