Connecting between Fabric SQL Database and Azure Function App

Hi Pablo82 
Thanks for reaching out to Microsoft Fabric Community Forum.

The 'HYT00 Login Timeout expired.' error usually indicates a network connectivity issue rather than a problem with the connection string or code.

Since your Function App is integrated with a VNet, please verify the following:

• Ensure the managed private endpoint created by the Service Connector is approved in the Fabric workspace (Workspace -> Networking - Managed private endpoints).
• Confirm that any NSG or firewall rules allow outbound traffic on TCP port 1433 to the Fabric SQL endpoint.
• If you are using Managed Identity authentication, make sure the Function App’s identity has been granted access to the Fabric SQL database. You can do this from the Fabric portal by sharing the database with the identity and assigning an appropriate role.

Reference :
 Integrate SQL database in Microsoft Fabric with Service Connector | Microsoft Learn
Connect to Your SQL Database - Microsoft Fabric | Microsoft Learn
Authentication in SQL database - Microsoft Fabric | Microsoft Learn

Hope this helps!!
Thank You.