See this question for reference.
After spending time troubleshooting this issue, it appears that there's no way for a LAMP server with Wordpress to communicate with an Azure-SQL database, or if there is already a library for this:
Currently, the official WordPress distribution only supports the MySQL and MariaDB database engines.
Note that MariaDB is a drop-in fork of MySQL. The same functions are used with both, so WordPress really only supports a single type of database server.