It's documented. There are a set of features in SQL Server that make less sense at the databaase level. Linked Servers are instance level, so some architectural change is needed to the database to get these to work. They're part of the same type of work that would get us contained jobs as well. Fingers crossed someone does this.

For your situation, I'd look at the serverless stuff. Not sure what this is in AWS, but it's there. In Azure, it's Azure Functions. You should be able to write a query on a timer that gets from MySQL, inserts to SQL Server. I'd think that wouldn't be too hard.'

Maybe this: https://stackoverflow.com/questions/37215069/azure-functions-database-connection-string
or this: https://stackoverflow.com/questions/44620692/unable-to-connect-to-azure-mysql-database-through-azure-function-c-sharp