When you deploy code to azure, were all existing files/ddl are cleared? it could be that old dlls still on the app service (not cleaned).

Also check the zip or folder of build/published package locally to see if both System.Data and Microsoft.Data dll are actually both there.

Regarding The exception occurs when connection string is parsed, probably you mean `not parsed' so gives exception above? If local uses Microsoft.Data, the app service should too. check the difference in debug and release folder to see if all dlls are same.