Hello David B,
Welcome to the Microsoft Q&A and thank you for posting your questions here.
Regarding the upgrade of any Azure SQL Database resources that use version 2014-04-01 APIs to a newer stable version is a known issue, and according to your questions:
What do I have to do to upgrade any Azure SQL Database resources that use version 2014-04-01 APIs to a newer stable version?
You need to update any applications, tools, scripts, or programs that use the 2014-04-01 API version to a newer stable version before October 31, 2025. Here is a similar solution: https://learn.microsoft.com/en-us/answers/questions/1115653/action-required-upgrade-azure-sql-database-2014-04
What specifically needs to be upgraded?
Any API calls made within the SQL DB blade or via Azure Automation that use the 2014-04-01 API version. Details on the API - https://community.spiceworks.com/t/azure-sql-database-2014-04-01-apis-will-be-retired-on-31-october-2025/947566
How would I find the resources that need to be upgraded?
According to your explanation, you said you handled SQL for customer on Azure, so review your application code or API calls to see which version is specified, you can do this in the Azure Portal, navigate to your subscriptions and check the registered resource providers for "Microsoft.Sql". Similar answer is here - https://learn.microsoft.com/en-us/answers/questions/2039548/action-required-upgrade-azure-sql-database-2014-04
Also, you asked.
How do I upgrade said resources?
To upgrade, you will modify the API version parameter in your API calls to a newer version as stated here -https://community.spiceworks.com/t/azure-sql-database-2014-04-01-apis-will-be-retired-on-31-october-2025/947566 and use the Azure Portal to browse to the server you want to upgrade by selecting BROWSE ALL > SQL servers, and then selecting the desired server. Follow the prompts to upgrade the server as stated here - https://github.com/Huachao/azure-content/blob/master/articles/sql-database/sql-database-v12-upgrade.md
I hope this is helpful! Do not hesitate to let me know if you have any other questions.
Please don't forget to close up the thread here by upvoting and accept it as an answer if it is helpful