@Lee Thanks for posting your question in the Microsoft Q&A forum.
You don’t need to worry about the databases if you’re only connecting to them via connection strings for your websites.
The retirement notice is specifically about the API version used for managing and interacting with Azure SQL Database resources programmatically.
Since you mentioned that you haven’t used the 2014-04-01 API since initially creating the databases and are just using them as normal databases, you should be fine.
The notice is about updating any scripts, tools, or programs that might still be using the old API version to manage the databases
Additional resources
https://github.com/mgnoonan/RssFeeder/issues/336
Regards
Geetha